Dan Ndoye opened the scoring in the third minute of what was largely a dominant first half for the visitors, who came to rue their wasted chances when Daichi Kamada drew the sides level with his first Premier League goal in the 41st minute.
Jefferson Lerma nodded Palace into the lead in first-half stoppage time and Yeremy Pino added a cushion just before the hour mark.
It was a first home Premier League victory for boss Pierre Sage, who was appointed following the summer exit of Glasner, the man who led Palace to trophies in the FA Cup, Community Shield and Conference League.
Glasner’s decision to join Forest in the wake of tension between the clubs – sparked by the legal fallout from Palace’s demotion to the Conference League before the 2025-26 season – came as a surprise to many.
The Forest boss, and returning right-back Daniel Munoz, were nevertheless greeted warmly on Sunday, save a “you’re getting sacked in the morning” chant minutes before the final whistle.
The opening goal was a poor one for Palace to concede, the product of an easily-intercepted Anan Khalaili header intended for Eagles goalkeeper Walter Benitez, filling in again for injured captain Dean Henderson.
Instead, Ndoye accepted the gift and gave Benitez no chance when he fired into the far corner.
Jorgen Strand Larsen drew an alert Matz Sels save when he tried to prod in an equaliser five minutes later, then had a follow-up blocked by an outstretched Murillo, while Quinten Timber failed to control an effort just after the 10th minute.
It was all Forest for a lengthy spell, including a header from the unmarked Ndoye requiring an excellent reaction from Benitez to tip it over his crossbar, before Munoz, who would have wanted to do better, directed a half-volley wide.
Morgan Gibbs-White struck the underside of the crossbar with 10 minutes remaining in the half and Liam Delap was denied on the rebound after Benitez managed to scramble his body in the path of his volley from point-blank range.
Those spurned opportunities would come back to haunt Forest as Kamada equalised after some good link-up play from the hosts, who worked the ball to Strand Larsen.
He picked out Timber, who found Kamada with a backheel to slot in the leveller – confirmed by a VAR check – in the 41st minute.
An unmarked Tyrick Mitchell nearly fired the hosts in front early in first-half added time with an effort from distance, tipped over by Sels, before Lerma did give Palace the lead.
It came from a corner and an ensuing scramble from Adam Wharton’s cross, which was met by the Colombian who planted the ball through a crowd between the legs of the Forest keeper.
There was a Ndoye miss before the break, another squandered chance the visitors would come to regret when Pino extended Palace’s lead in the 59th minute.
Sels had, moments before, saved a Strand Larsen effort and the ball fell favourably for the Spain international, who prodded it home – a goal also upheld by VAR.
Benitez produced another fine save late on to deny Chris Wood any chance of opening the door to a Forest comeback.