Connacht pulled away from Munster in the final quarter to claim the spoils on a wet and windy afternoon at the Sportsground.
The sides were level going into the final quarter but two more penalties from former Munster player JJ Hanrahan and the only try of the game in the closing stages from prop Jack Aungier ensured Munster left Galway empty-handed.
Munster were forced to make a couple of pre-match changes when hooker Eoghan Clarke and lock Fineen Wycherley joined an already lengthy casualty.
Graham Rowntree’s men were then forced to make two further changes in the opening half when tighthead Oli Jager, with a head injury, and No.8 Jack O’Donoghue, with a knee injury, were stretchered off.
Gavin Coombes, who switched to the second row after Fineen Wycherley’s withdrawal, had a try ruled out after three minutes when he charged down Caolin Blade’s clearance but was adjudged to have a knee over the dead-ball line by the time he touched down after sliding through.
Hanrahan got Connacht off the mark with a penalty after 17 minutes but Tony Butler levelled five minutes later with a penalty.
Munster tried to use the strong wind and Butler executed a superb 50:22 after 26 minutes but they were unable to make the chance count.
Butler edged Munster back in front seven minutes from the break without another penalty and Connacht ended the half down a man when winger Byron Ralston was binned for a tackle on O’Donoghue.
Connacht, with the wind behind them on the restart, levelled when Hanrahan converted a 35-metre penalty Munster hit back and worked their way upfield with a few penalties before Butler edged them back in front after 58 minutes.
Hanrahan levelled three minutes later when Hanrahan converted from 25 metres to tie the game at 9-9. Connacht went ahead 14 minutes from time with another penalty and Hanrahan slotted the penalty from 25 metres to lead 12-9.
They doubled the lead eight minutes from time when Hanrahan landed his fifth penalty from distance, and Munster were denied a bonus point when replacement prop Aungier got over for the only try of the game in the closing minutes.
Munster: Simon Zebo; Calvin Nash, Antoine Frisch, Rory Scannell, Shane Daly; Tony Butler (Sean O’Brien, 72), Conor Murray (Paddy Patterson, 75); Jeremy Loughman (Josh Wycherley, 78), Scott Buckley, Oli Jager (inj, John Ryan, 11); Gavin Coombes, Tadhg Beirne (C); Tom Ahern, John Hodnett (Brian Gleeson, 78), Jack O’Donoghue (inj, Alex Kendellen, 40).