Alan Knill's men slipped to ninth after losing their last three games but got back to winning ways with a deserved victory at Meadow Lane.
Bury were on top for long periods before defender Cresswell headed home in the 78th minute to send the Shakers back into the play-off places.
The visitors looked determined to turn their fortunes around and put in a dominant first-half performance.
Mike Jones threatened as early as the fifth minute, firing narrowly wide after being put clean through.
Stephen Dawson then went close while Elliott Bennett was denied by home keeper Russell Hoult.
Andy Morrell was recalled up front in place of Chris O'Grady and fired wide from inside the box in the 25th minute.
The hosts posed little threat in the first half, with Myles Weston and Richard Butler shots easy for Bury keeper Wayne Brown.
Bury were unable to maintain their momentum through the second period and Butler twice went close shortly after the restart.
Knill sent on O'Grady for top scorer Andy Bishop in a bid to revive his attack and within a minute the Shakers broke the deadlock.
Jones won a free-kick in the left channel and Cresswell rose highest to head home Jones' delivery from six yards out.
County could have claimed a draw at the death but Bury breathed a huge sigh of relief as Weston turned his shot wide from close range.
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