Kick-off was delayed by 50 minutes after a member of the Parachute Regiment crash landed on to the roof of a stand instead of the intended target on the half-way line.
The delay didn't appear to affect Burnley too much in the early stages of the match with Wade Elliott crossing for Joey Gudjonsson to glance a header wide of the near post.
Richard Wright then tipped a Clark Carlisle header over the crossbar and then saved smartly from Chris Eagles.
A fine move down the left involving Martin Paterson and Robbie Blake led to another strike by Eagles which was pushed for a corner.
That was taken by Blake and from which a header from Elliott was tipped against the crossbar by Wright.
But goals change matches and Ipswich took the lead on 34 minutes with their first real threat as the Burnley defence failed to clear a corner and the ball was swept home by Liam Trotter with the aid of a deflection.
Ipswich extended their lead five minutes before half-time when Alan Lee's cross from the right was turned into his own net by right-back Graham Alexander.
Ipswich should have wrapped the game up seven minutes into the second half when Alan Lee went clear of the Burnley defence only for Brian Jensen to make a save.
Burnley manager Owen Coyle made a double substitution two minutes later, replacing Blake and Gudjonsson with Ade Akinbiyi and Kevin McDonald.
But it was Jensen who again denied Lee, turning the striker's shot behind for a corner.
Paterson came close to pulling a goal back when Wright fumbled a cross from Eagles but the striker lifted the rebound over the crossbar.
Another piece of comical defending three minutes from time saw left-back Stephen Jordan head a long free-kick from Richard Naylor beyond Jensen to complete the scoring.