Mitch Duke met a Craig Goodwin free kick at full stretch and cut the ball back to set up Jackson Irvine for a sharp finish into an open goal in the 13th minute -- albeit replays indicated that VAR would likely have been ruled the goal out for offside had it been in operation.
Michael Estrade spurned a golden chance to level two minutes later, and the South Americans restored parity in the 23rd minute when the host couldn't clear a free kick. Jeremy Sarmiento escaped the pressure of debutant Aiden O'Neill and sent in a ball that Torres rose over Irvine and Milos Degenek to head home.
Australia regained the lead in the 32nd minute when a poor backpass from Sarmiento's Brighton & Hove Albion teammate, Moises Caicedo, invited Irvine to press and tackle Piero Hincapie, with the ball falling kindly for Awer Mabil to hammer a first-time effort beyond Moises Ramirez.
Australia had what looked to be a clear penalty waved away for a dubious offside in the second half but nonetheless found a third in the 84th when Aziz Behich found Garang Kuol for an open, close-range tap-in. Again, replays indicated that the assistant referee may have erred in keeping the flag down.
1. Post-World Cup vibes
There was a definite sense that Graham Arnold and the Socceroos were playing with house money during this international window - and not just because it was the coach's first game after signing a lucrative contract extension that will take him to the end of the 2026 cycle.
Coming off the back of a World Cup in which they stunned most onlookers both in Australia and around the world by reaching the round of 16, the two-game series with Ecuador was styled as a "welcome home" celebration, a chance to recognise and commemorate the achievements of the side in Qatar. Beyond that, the infusion of further young talent and potential debutants into the side after the refreshing of the squad led to further excitement, and the absence of squad members Aaron Mooy, Mat Leckie, Ajdin Hrustic and Jamie Maclaren through injury gave cover for any disasters.
The result almost felt like an afterthought during the build-up, as were the merits of the Ecuadorians themselves, who are without Enner Valencia for their tour Down Under. It was unlikely that anything other than a complete thrashing would have really done much to merit raised eyebrows.
But now, a 3-1 win over a side that qualified automatically from the crucible that is CONMEBOL during the last cycle will only add to the feelings of positivity and expectation building around the Socceroos heading into the coming years.
2. Young talent time
Inevitably at the start of every new World Cup cycle, there are predictions about what the squad will look like in four years' time. Who among the current crop will step up and replace the leaders that inevitably move on, and which talent will emerge themselves as members of the squad? Some of that talent was on display on Friday.
Established as the first-choice centre-back pairing in Qatar, the duo of 24-year-olds Harry Souttar and Kye Rowles again took up position in the XI, with Keanu Baccus and O'Neill starting in the midfield alongside.
After Australia won out for his services over competing eligibility from Scotland, Peru and England, Alex Robertson made his debut and showed flashes of the talent that has earned him the opportunity to train with Manchester City's first team, including a role in the build-up to his nation's third goal.
And after a difficult time in Scotland since moving to Hearts on loan from Newcastle United, Kuol's latest goal off the bench was clearly a weight off the shoulders of a player that's carrying a fair weight of expectation.
3. Bring the heat
Australia's second goal and the great spell they enjoyed afterward encapsulated how this team has come to operate at its best under Arnold: high pace, high energy and straight down opposition throats.
Irvine's quick move to step and press Hincapie after Caicedo sold him into trouble immediately led to a goal and the following exchanges were played at the kind of frenetic pace in which the Socceroos revelled and the South Americans didn't appear to be much enjoying. Arnold frequently talks about his side being full of energy and fearless in approach and this, mostly, is what he means; his side's best moments throughout the game came when they were playing at a full throttle. The Matildas have found success in the same manner recently -- maybe that's the "Aussie DNA" Arnold he likes to talk about.
However, it wasn't all like that. On other occasions, the Socceroos were more than content to retreat into the armoured tortoise of a 4-4-2 defensive block, inviting the opposition to come forward and sometimes sitting back so deep that they were almost at risk of falling between the couch cushions. It was in these periods when the Ecuadorians were able to get their foot on the ball, face the goal, and work on their combinations in their half where they were clearly in the ascendancy. This, in turn, also affected which areas of the pitch the Australians were winning the ball in. Often collecting the ball deep in their half, inviting the Ecuadorians to press the Australian backline and creating several nervy moments.
Therein lies one of the conundrums for Arnold heading into the next four years. His conservatism with unleashing his team came back to bite him on a few occasions during Australia's up-and-down qualification campaign for 2022 -- particularly in a qualifying loss to Japan that forced them into the playoffs. On Friday, signs were shown that this Socceroos side has the scope to bring more heat in the years ahead.
Best and worst performers
Jackson Irvine, Australia: Deployed further up the pitch in a role that allowed him to utilise his ability to get into the penalty box and looked dangerous whenever he did.
Harry Souttar, Australia: Popped up on numerous occasions to steer away Ecuadorian attempts to get in behind the defence and was his now customary pillar of strength.
Jeremy Sarmiento, Ecuador: A constant danger during the first half and set up Ecuador's goal. However, he was forced off with an injury in the 30th minute -- coach Felix Sanchez saying postmatch that he had been sent to hospital for scans.
Moises Caicedo, Ecuador: With Valencia out, there was more scope for Caicedo to serve as a focal point for his side but he failed to stamp his authority on the game. Played the soft backpass that led to Australia's second goal.
Piero Hincapie, Ecuador: Wasn't helped by Caicedo's backpass, but still surrendered the ball to Irvine which led to Mabil's goal.
The anti-VAR crowd: Multiple incidents likely would have been overturned had VAR been in action, demonstrating the value that it can bring.
Highlights and notable moments
Irvine put Australia ahead early on, although it might have been a different story if VAR was in effect.
Sarmiento put the ball on the head of Torres 10 minutes later to level proceedings.
Irvine's press led to Mabil putting the Socceroos back on top, and they kept hold of their lead.
After the match: What the players/managers said
Graham Arnold on the youngsters: "Let's not get too carried away, those kids need a heap of experience and plenty of game time at their clubs. The senior boys are doing it every week and you can see the example that they're sending."
Alex Robertson on his ambitions with Australia: "You've got to reach for the stars and win a World Cup, you never know what's going to happen. I think we can do some really big things in the future, so why not say it?"
Felix Sanchez on his first game in charge of Ecuador: "For us today, it was our first game of a new cycle. It's a new start. We had a few sessions to work with the players. It was a test for us. We have to adjust many tactical things, but that's normal. The quality of the players is there and we are optimistic."
Key stats (provided by ESPN Stats & Information)
Australia has now equalled the ledger in their all-time series with Ecuador, avenging their 4-3 defeat in the only other meeting between the two sides back in 2014.
Australia has now lost just one of their last 11 games at home, although Friday was their first win in Sydney since 2017.
Graham Arnold became the first coach since Frank Farina to lead the Socceroos into their opening game of back-to-back World Cup cycles.
Both nations will head to Victoria, where they will play the second of their two-game series at Melbourne's Marvel Stadium on Tuesday.