The visitors, who had lost all four away games in the league and cup this season, actually had the better chances to win after the break so pressure continues to build on Blues boss Jim Magilton.
Magilton was derided with chants from the home fans when he replaced goalscorer Stead in the second half and his team were booed off at the end.
The game had begun quietly and took 20 minutes to get going before Richard Wright saved efforts from Nick Carle and Paul Ifill.
Town then went ahead on 23 minutes when Jon Walters' cross was cleverly dummied by David Norris to leave Stead free and he coolly slotted home.
Wright made a fine save to tip over a Moses header, but from Ben Watson's ensuing corner Wright and Alex Bruce impeded each other and Moses nodded the loose ball home.
Julian Speroni made a fine tip over to deny Kevin Lisbie's firm header, but Palace had the better first half chances, notably when Clint Hill had one effort charged down and then blazed the rebound over.
Both teams found it hard to get efforts on target after the break with the worst miss being when Watson shot wide from six yards from an Ifill cross.
Wright saved easily from man of the match Moses and Town old boy Shefki Kuqi, while the hosts could have undeservedly snatched it late on as sub Owen Garvan twice flashed dangerous crosses across the face of goal.