A virtuoso first-half performance from Nicky Robinson guided Gloucester an 18-3 triumph - only their second Premiership win at Bath and denied the home team a record ninth successive home victory.
At a rain-soaked Recreation Ground the former Wales fly-half tormented Bath with his tactical kicking and scored a crucial 25th-minute try. He also kicked a conversion and two penalties.
Bath's high-tempo game was undermined by spilled possession and their only answer was an Olly Barkley penalty.
Neither team scored in the second half.