Tissoudali fired home in the 76th minute at the end of a counter attack in a rare foray forward for the visitors at the Stade des Martyrs.
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Morocco will be favourites to progress with the second leg to come in Casablanca on Tuesday, and the aggregate winner qualifying for November's finals in Qatar.
The Congolese had led from the 12th minute after Yoane Wissa opened the scoring, but they wasted several other good chances while Morocco squandered a second-half penalty.
Wissa, the French-born attacker who plays for Brentford, cut inside off the right wing and saw his shot take a wicked deflection off Morocco's captain Romain Saiss before nestling in the back of the net.
It was the perfect start for the home team, who are attempting to qualify for the finals for the first time since 1974.
Cedric Bakambu was denied a chance to extend the lead just before the half-hour mark by Morocco goalkeeper Yassine Bounou while Morocco made their first effort on the home goal just before halftime when Youssef En-Nesyri headed wide.
Wissa came agonisingly close to a second goal straight after the break, firing narrowly wide, but then Bakambu handled in his own area while attempting to defend a corner, handing Morocco a way back into the game.
Ryan Mmaee, however, blasted his 55th-minute spot kick high over the crossbar.
Tissoudali spared his blushes with the equaliser after a long ball forward was chested down by Ayoub El Kaabi into the path of the Belgian-based striker, who blasted home.
Congo's woes were extended five minutes from fulltime when wingback Glody Ngonda was sent off for a second caution and will miss the return leg.
The build-up to the match was overshadowed by a complaint by Morocco to the Confederation of African Football that local fans had disrupted their training by invading the pitch and that buses they had booked to transport their squad on arrival in Kinshasa on Tuesday failed to turn up, leaving them stranded at the airport.
The Congolese football federation said buses were available for their visitors.