Mick McCarthy's men opened the scoring in fortuitous circumstances as a lack of communication between goalkeeper Lee Camp and defender Danny Collins saw Guirane N'Daw nip in to score.
Dexter Blackstock squeezed home an equaliser in the 58th minute, but Town regained the lead three minutes later when Luke Hyam netted the rebound from DJ Campbell's penalty which had been saved by Camp.
The Forest goalkeeper was lucky to be on the pitch after rushing out to stop Campbell when he was bearing down on goal in the 16th minute.
Substitute Daryl Murphy sealed the points at the death with a neat finish.
A lively start from Town saw them create the first opening of the game. Lee Martin floated in a cross for the unmarked Tommy Smith but his header was straight at Camp.
McCarthy had his head in his hands as Camp escaped with just a yellow card after taking out Ipswich striker Campbell as he raced through shortly afterwards.
The home side got the goal their pressure deserved in comical circumstances on the half hour. A mix-up between Collins and Camp allowed N'Daw to sneak in and score.
The goal seemed to spark Forest into life and they came agonisingly close to an equaliser in the 42nd minute when Billy Sharp took advantage of a slip from Bradley Orr to rattle the crossbar from Alan Hutton's cross.
Daryl Murphy came on for debutant Tyrone Barnett in the second-half and was immediately involved, firing in a shot which took a deflection and almost caught out Camp who gratefully gathered.
But Forest levelled shortly afterwards as Reid found Sharp and the striker managed to get the ball across to Blackstock who poked home from six yards.
Their joy was shortlived, though, as Ipswich were awarded a penalty when Campbell went down in the box under challenge from Collins. Camp made a superb stop from Campbell's spot-kick but Hyam followed in to score.
Ipswich sealed a much-needed win in the last minute when Murphy dispossessed Reid and was allowed to carry the ball into the box where he coolly slotted past Camp.