When they declared on 201 for seven they will have felt more confident of winning than losing, given their hosts had a target of 422.
A century from Joe Burns - following on from a first-innings 97 - gave Queensland a chance, though, and Bresnan was needed to come on at the end and steady the ship.
Although unable to take any wickets - Moeen Ali took five for 125 - Bresnan bowled tightly at the end and ensured Queensland fell eight runs short of victory, having needed 18 off six overs at one stage.
Bresnan is hoping to be called up to join the Test squad for the second clash with Australia in Adelaide, having missed the opening defeat in Brisbane as a result of his recent back surgery. His second-innings figures were none for 41 off 16.
Sam Robson again impressed with the bat, with the Australia-born Middlesex man adding to his first-innings ton with a smart 65, the same score as Ben Foakes.
Burns was given ample run-chase support by Corey Barsby (59) and Chris Sabburg (46) but they had to settle for a draw.
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