The Hoops had previously drawn 0-0 at Reading and beaten Birmingham 1-0 at home under Ainsworth, but they had no answer to Stead, who netted his goals within seven minutes of coming on.
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.