Bancroft, back in Test contention after he was banned for his part in a ball-tampering scandal in Cape Town in March last year, opened the batting at Hampshire's headquarters and his innings helped the Graeme Hick XI beat the Brad Haddin XI by five wickets.
Bancroft was the only batsman apart from David Warner - also banned for his part in the affair - to pass fifty in the match, with his innings coming just a day before Australia announce their Ashes squad on Friday.
Bowlers dominated as a match scheduled for four days ended on the third with former captain Steve Smith, the third member of the banned ball-tampering trio, managing scores of just eight and nine in his two innings at the Rose Bowl.
The Haddin XI were all out for 105 and 170, while the side of fellow assistant coach Hick were dismissed for 120 before they reached their target of 156 in their second innings for the loss of five wickets.
Fast bowlers Pat Cummins and Mitchell Marsh each took six wickets in the match, while veteran seamer Peter Siddle bagged five.
The first of a five-Test series between England and Australia starts at Edgbaston on August 1.
Australia hold the Ashes but have not won a Test series away to arch-rivals England since 2001.