The striker, signed in August from Sheffield United, took his tally for the season to five and almost completed a hat-trick in the final seconds when his 30-yard free-kick crashed against the post.
Both teams displayed some neat passing football on a surface made slick by continuous rainfall, that lacked a cutting edge, with the main opportunities coming from set-pieces.
Gareth McAuley almost got on the end of an Owen Garvan free-kick for Ipswich before Lee Cook curled a free-kick against the Ipswich bar.
Richard Wright then produced a superb diving save to keep out a Martin Rowlands header from Daniel Parejo's curling cross.
Radek Cerny denied David Norris's 20-yard effort before Wright saved from Samuel Di Carmine and then turned away Parejo's dipping 25-yard free-kick.
Cerny also saved from Jon Walters and Garvan had a fierce low drive blocked to end the half.
Ipswich stepped things up after the break, as Walters shot over and Cerny saved a Walters header and a Kevin Lisbie drive.
Wright tipped over an inswinging Parejo corner, and Cook flashed a drive narrowly wide, before Stead took centre stage.
He opened the scoring on 73 minutes when McAuley and sub Pablo Counago helped on a Garvan free-kick and, although Cerny blocked Stead's initial shot, he nodded in the rebound from six yards.
Garvan was involved again for the second goal, his curling corner met with a bullet header by Stead which flashed beyond Cerny.
Counago had two great chances to seal the points but failed to take them before Stead thundered a stoppage-time free-kick against the woodwork with Cerny beaten.