Kelvin Davis parried a rasping shot from Jon Oster and kept out Sean Gregan's header as Leeds started well.
But Neil Sullivan saved well from Kevin Horlock and it was 1-0 soon after the interval when Bent netted after Shefki Kuqi's shot was parried by the keeper.
Kuqi then headed Jim Magilton's cross wide, while Davis produced a fine save from Brian Deane's late drive.
Ipswich boss Joe Royle:
"With Tommy Miller's injury I had already made up my mind we were
going to go with three up front and we passed the ball better.
"We defended well, and we have just had our third clean sheet
in four games. We have said if we do keep clean sheets then we will have a great chance because we usually score.
"The first goal here is now becoming so important. We saw that with Burnley
when we spent 70 minutes trying to get back and also when we went behind against
Leeds boss Kevin Blackwell:
"Ipswich were hanging on at the end. With everything that is going on at the
club it is a tribute to the players.
"I felt my players played well and we pushed one of the top sides all the
way. There are plenty of sides that will come here and go away with nothing.
"Simon Walton has just turned 17 and turned in a good performance which is
why Premier League clubs are looking at him."
Ipswich: Davis, Diallo, De Vos, Naylor, Wilnis, Miller (Bowditch 48), Magilton, Horlock, Westlake, Bent, Kuqi.
Subs Not Used: Price, Richards, Counago, Collins.
Goals: Bent 51.
Leeds: Sullivan, Kelly, Carlisle, Butler, Pugh, Wright (Joachim 73), Gregan, Walton, Healy, Oster, Deane.
Subs Not Used: Carson, Richardson, Lennon, Kilgallon.
Booked: Carlisle, Walton, Wright.
Ref: A Wiley (Staffordshire).