After dominating a first half that saw Kieran Trippier shave the outside of the post with a free kick, Newcastle must have gone in at the break wondering what they needed to do to score after a flurry of chances were thwarted.
Deploying a tight five-man line across the back, Bournemouth's defence came out for the second half determined to shut down the spaces that led to those chances, and their plan worked admirably.
Things then went from bad to worse for the hosts when Philip Billing scored for Bournemouth in the 62nd minute, guiding in a deft volley with his left foot to briefly silence the home crowd.
However, that lead did not last long as Jefferson Lerma was penalised following a VAR review for handling Trippier's cross in the box, and Isak stepped up to slam the spot kick past Neto.
It was Isak's first goal at home for Newcastle since joining from Real Sociedad in August for a reported club-record fee of £59 million.
Newcastle's lack of penetration proved costly as they struggled to create despite enjoying the lion's share of possession, with Joelinton's weak stoppage-time header the closest they came to threatening Neto's goal again.
Bournemouth rose two places from 14th to 12th on eight points while Newcastle's fifth stalemate in seven league games moves the Magpies up to 10th in the table, also on eight points, with their fans booing at the final whistle.
"Today I thought we dipped," manager Eddie Howe told BEIN Sports. "I thought it was away from our highest level, and if we hit anywhere near our highest level, we would have won today.
"Right from the start, we didn't have that zip and feel about us that we have done at times this season," he added.
Bournemouth caretaker manager Gary O'Neil told the BBC that he expected to find out about his future in the coming week after a good result at Newcastle.
"I am pleased the boys got something out of it because they put in a hell of a shift," he said.