Connacht led 12-7 at the interval with Fionn Carr getting them off the mark in the sixth minute, following Niva Ta'auso's intercept on the Connacht 22.
Ian Keatley converted before Keith Matthews extended Connacht's lead after half an hour with their second try.
Gloucester responded with a try from new signing Nicky Robinson to leave it 12-7 at the break.
The hosts took the lead shortly after the restart when prop Nick Wood got in for a try which Robinson converted.
James Simpson-Daniel extended his side's advantage before Connacht responded with a pushover try from recent signing Mike McComish.
Troy Nathan tagged on the conversion to put the visitors within two points of the lead but Gloucester sealed the win with a penalty from Robinson and a late try from Jonny May.
Meanwhile, the Connacht Rugby Open Day, in aid of Special Olympics Ireland, which was scheduled to take place this Sunday afternoon (August 23) has been postponed due to the bad weather.
The event will be rescheduled for a later date. Connacht Rugby would like to apologise for any inconvenience caused.
CONNACHT: Troy Nathan; Brian Tuohy, Niva Ta'auso, Keith Matthews, Fionn Carr; Ian Keatley, Fionn Murphy; Brett Wilkinson, Sean Cronin, Robbie Morris, Andrew Browne, Bernie Upton, Mike McCarthy, Ray Ofisa, John Muldoon.
Replacements used: Mike McComish for McCarthy (half-time), Adrian Flavin for Cronin (56 mins), Jamie Hagan for Morris (59), Ronan Loughney for Wilkinson (69), Tiernan O'Halloran for Keatley (71), Mike Swift for Ofisa (73).