A Robbie Keane strike and an own goal sealed victory for Leeds on an afternoon when little went right for Ipswich.
The home side dominated possession, pinning Leeds back for long periods, but defensive errors in the first half cost them two goals.
Mark Venus put into his own net and Keane capitalised on a catalogue of mistakes to put Leeds two up at the interval.
Venus managed to grab a consolation after the break with a stunning free-kick.
But Marcus Stewart was controversially sent-off to effectively end Ipswich hopes.
The striker was late and reckless when he fouled Leeds defender Ian Harte, but a red card seemed excessively harsh.
Ipswich dominated the first-half, far more mobile and imaginative in midfield and attack than their visitors who defended in depth and hoofed clear when necessary.
The home side had a good chance after 10 minutes, when Stewart evaded Lucas Radebe inside the area, but Nigel Martyn got down well to save his shot.
Matt Holland tested Martyn again minutes later with a diving header, but Leeds then stunned their hosts by scoring.
Lee Bowyer fired in a cross from the right, Venus miscued his clearance to send the ball goalwards.
Ipswich piled forward in search of an equaliser and Jamie Clapham had an excellent chance to equalise after 38 minutes.
James Scowcroft powered into the area from the right and squared, finding Clapham on the far post.
But the winger could not get a good contact and Leeds cleared.
The miss proved costly, as Leeds hit Ipswich with a second sucker punch.
Keane was again the scorer, converting the easiest of opportunities after a series of Ipswich mistakes.
First Mills was allowed to break down the right wing unchallenged and cross.
Then Venus and Titus Bramble missed the ball allowing Keane to fire home from close range.
After the break, Holland went close with a searing shot on the run from 20 yards and Venus helped to atone for his earlier mistakes by scoring with a stunning 25-yard free kick.
But Ipswich's cause was hardly helped when leading scorer Stewart was shown the red card for a foul on Harte after 74 minutes.
Stewart took Harte's legs away after the Republic of Ireland international had turned him inside out on the left wing.
The foul was reckless and late, but did not seem to warrant the red card that referee Peter Jones wielded.
Mark Viduka thought he had scored a third goal for Leeds late on, but his effort was disallowed by a late flag.
Ipswich: Richard Wright, Croft, Clapham, Venus, Hreidarsson, Bramble, Jermaine Wright, Holland, Scowcroft, Stewart, Armstrong. Subs: Branagan, Naylor, Reuser, Brown, Abidallah.
Leeds: Martyn, Harte, Mills, Radebe, Ferdinand, Matteo, Bowyer, Dacourt, Batty, Viduka, Keane. Subs: Robinson, Wilcox, Smith, Bakke, Burns.
Referee: P Jones (Loughborough).