Josh Carson's first goals for the Club gave Town a third successive victory in front of the biggest League crowd at Portman Road this season.
The 17-year-old, who was making only his third appearance for Blues, opened the scoring on 38 minutes with a right foot effort and was then in the right place to find the net from close range midway through the second-half.
Patrick McCarthy gave Palace a lifeline and Town had a couple of anxious scares, with Neil Danns wasting a glorious chance to equalise in added on time but Blues held on for the points.
Town stayed with the side that beat Burnley last weekend, while Palace had only one of their former Blues in their starting line-up, Darren Ambrose.
David Norris sent the ball flashing across the Eagles' goal inside the first two minutes, Grant Leadbitter and then Carson trying their luck from distance but off target.
Connor Wickham also failed to test Julian Speroni with a right foot effort after Palace switched off at Mark Kennedy's throw, the Argentine 'keeper called into action seconds later though to deny Leadbitter's 25 yarder.
Ambrose sent a free-kick into the wall after Damien Delaney's foul on James Vaughan in Palace's first effort, the Eagles threatening on the break during the opening half, Ambrose lifting the ball over Lee-Barrett but wide of the far post.
At the other end, Carson's superb delivery just evaded Jason Scotland and Wickham, while Lee-Barrett beat out Ambrose's 25 yard drive.
Wickham hit the sidenetting after Carlos Edwards' shot had fallen into his path before Blues got the breakthrough eight minutes before the break, Carson cutting in and sending a right footer into the far corner.
Norris was inches away from extending Town's lead as soon as the second-half got underway, his left foot effort going just wide, then Edwards went even closer with a 20 yarder against the post.
Palace could have been level on 52 minutes though, Lee-Barrett saving well from Vaughan but the ball fell to Kagisho Dikgacoi - the midfielder failing to convert the rebound from the edge of the box.
Speroni kept out Wickham's header at the far post, Lee-Barrett then doing the same low down from an excellent Vaughan effort.
Delaney picked up the first yellow card of the game after catching Neil Danns, Ambrose then having a great chance to equalise on 64 minutes but Lee-Barrett was equal to the task again.
It proved a crucial save because a minute later Town doubled the advantage, Delaney caused confusion in the Palace box from a corner and Carson
blasted the ball in from inside the six yard box.
Kieron Dyer replaced Scotland, Wilfried Zaha and Sean Scannell on for Ambrose and Vaughan for Palace on 70 minutes in the first changes and a minute later the Eagles were back in the game, McCarthy getting on the end of Kemy Agustien's long free-kick and blasting past Lee-Barrett.
Zaha fired wide of the far post as the Eagles threatened an equaliser on 77 minutes, Leadbitter then booked for a foul on Danns.
Colin Healy replaced Jimmy Bullard on 83 minutes, Kieron Cadogan introduced for Agustien as Palace completed their changes.
Leadbitter's free-kick was deflected wide after Dyer had been fouled, Speroni forced to push Delaney's header around the post from the corner.
Palace had a final chance to equalise when Danns sent a left foot effort wide of the goal from a great position, Zaha then blazing over from the angle before a final blast of referee Graham Salisbury's whistle gave the points to Blues.
Town: Lee-Barrett, Edwards, McAuley, Delaney, Kennedy, Carson, Leadbitter, Norris, Bullard (Healy 83), Wickham, Scotland (Dyer 70). Subs not used: Fulop, Drury, Peters, Civelli, O'Dea. Booked: Delaney, Leadbitter.
Palace: Speroni, Clyne, McCarthy, Gardner, Moxey, Ambrose (Zaha 70), Dikgacoi, Agustien (Cadogan 83), Danns, Vaughan (Scannell 70), Iversen. Subs not used: Price, Davis, Garvan, Mahon.
Att: 24, 378