The only goal of the game came right at the start of the second half and it was a spectacular effort.
Tommy Miller crossed from the right and with his back to goal, Stead fired in an overhead scissor kick that roared past Reading keeper Marcus Hahnemann.
Reading fans had been full of hope at the start as manager Steve Coppell made three changes from the side that drew against lowly Charlton in midweek.
Hahnemann replaced Adam Federici in goal, skipper James Harper returned in place of Marek Matejovsky and leading scorer Kevin Doyle made way for Dave Kitson, returning on loan from Stoke.
By contrast Ipswich, needing a good run of results to make the play-off places, were without star winger Jon Waters, who injured an ankle against Wolves in midweek.
Kitson made his presence felt after just three minutes and was unlucky not to put Reading ahead.
Gareth McAuley fouled Shane Long and from Glen Little's free-kick, Kitson sent a header thumping against the Ipswich crossbar.
Then a three-man move between Kitson, Brynjar Gunnarsson and Stephen Hunt forced Ipswich keeper Richard Wright to dive at Hunt's feet to make a brave save.
It was 24 minutes before Hahnemann was forced into action, diving to his left to gather a long-range effort from Alan Quinn.
Reading were soon back on attack with Long setting up a chance for Harper to fire a shot straight at Wright, but then Miller gave the Royals a fright when he fired high over the crossbar ten minutes before the break.
The early second-half goal really encouraged Ipswich and Kevin Lisbie was not far away from adding a second from Luciano Civelli's cross.
Reading then came very close to grabbing an equaliser in the 63rd minute when Little's cross was headed goalwards by Michael Duberry, but Ben Thatcher headed the ball away from the goalline.
With just over 20 minutes remaining, Coppell decide that it was time to bring Doyle into the game, replacing fellow Irish international Long.
But it was Little who had the next effort with a thumping drive that Wright safely held.
Then it was Hahnemann's turn to make a magnificent one -anded save from Lisbie 12 minutes from time as Ipswich tried to hit Reading again on the break.
At the end, Reading's disappointed fans booed their side off the pitch.