Ipswich created the first chance of the game at St James Park on Tuesday, but Jon Stead scuffed a shot wide after latching onto a long Brian Murphy goal-kick. Exeter should have gone in front when Matt Taylor met Ryan Harley's corner kick, but he planted his header over the crossbar.
Harley broke the deadlock after 54 minutes with a fine shot that flew across goal and went in off the far post.
Ipswich responded with intent and it took 10 minutes before they were level, when a cross from the right was headed in by substitute Ronan Murray.
The Tractor Boys were in control now and grabbed their second goal when David Norris lashed a low shot inside Paul Jones' near post.
However, Harley levelled things up when he picked the ball up 25 yards from goal and crashed an unstoppable shot that flew in off the underside of the Ipswich crossbar.
The Tractor Boys won it nine minutes into extra-time when Norris followed up to score after Stead's shot had been saved by Paul Jones.