Australia's first match under new coach Darren Lehmann saw the tourists ease to a six-wicket win over Somerset on the final day of four at Taunton on Saturday.
Usman Khawaja, Phil Hughes and vice-captain Brad Haddin all hit fifties as Australia, who on Monday replaced sacked former coach Mickey Arthur with ex Test batsman Lehmann just 16 days before the Ashes reached a target of 260 on the fourth afternoon.
That still gave Somerset and Ireland spinner George Dockrell take three for 78 in an innings where Khawaja top-scored with 73, Hughes added 50 to his first innings 76 not out and Haddin made an unbeaten 52.
Australia's second and final Ashes warm-up match is a four-day fixture against Worcestershire starting on Tuesday.
The first of a five-match Ashes series, with England holding the urn, starts at Trent Bridge, Nottingham, on July 10.