But after Jose Fonte scrambled Neil Warnock's men level, Jon Stead was unluckily sent-off to leave Keane's side a man short for 50 minutes.
Neil Danns and Victor Moses took advantage to score second-half goals for Palace and leave Ipswich looking over their shoulders at the relegation zone after a first defeat since October 3.
Keane's side started in confident mood and went close when defender Gareth McAuley headed high and wide from a corner.
The Town midfield were bossing the opening stages and it was no surprise when Peters stole in to score the 19th-minute opener. Palace full-back Clint Hill fouled Peters on the right-hand side and when the resulting free-kick was delivered into the penalty area, goalkeeper Julian Speroni scrambled the ball unconvincingly clear.
Damien Delaney instantly crossed the loose ball back into the area and the hapless Speroni could only drop the ball at the feet of Peters who gratefully volleyed into the open goal.
Stead then saw a powerful header saved by Speroni as Ipswich pushed for a second, but it was the home side who found a goal to level in the 38th minute after some more terrible defending.
Moses launched a long throw in the the heart of the penalty area, and Delaney hacked a hurried clearance into the back of Ipswich midfielder Owen Garvan.
Fonte was quick to react and he smashed the bouncing ball past Arran Lee-Barrett to bring Palace level.
If Keane was angered by the goal, his mood would not have been helped 60 seconds later when Stead was harshly shown a straight red card for a late, but not malicious, challenge on Freddie Sears.
Keane introduced teenage striker Connor Wickham at the break and again the visitors started well, Garvan shooting over after a smart break by Liam Rosenior.
But again Warnock's side responded to score against the run of play as Danns put them ahead in the 58th minute.
Delaney was at fault once more as he failed to clear a Darren Ambrose corner and Shaun Derry was able to chip the ball back into the area for Danns to take a touch and rifle past Lee-Barrett.
Peters and Rosenior both tested Speroni from long range as Ipswich continued to push but it was left for Moses to score the third in stoppage time.
The teenager has been heavily linked with a move to the Barclays Premier League during next month's transfer window and showed why when he collected Ambrose's pass to run in on goal and confidently finish.