In a hotly-contested encounter, the boot of JJ Hanrahan was of vital importance to Munster as his kept the scoreboard ticking over.
Jack O’Donoghue scored Munster’s only try while Jack Carty crossed for Connacht in the closing stages but it wasn’t enough.
After a hard-fought opening period, Munster got their first points through a Hanrahan penalty but Connacht closed the gap when Conor Fitzgerald scored one of his own.
With twenty minutes on the clock, after a penalty advantage Hanrahan slotted his second penalty in front of goal.
Munster soon sparked into action and it was O’Donoghue who crossed the try line after a series of pick and goes while Hanrahan added the extras.
Connacht never gave in and added to their tally through Fitzgerald before Hanrahan claimed another three points.
A move just before the break saw Connacht make ground into the Munster 22 and it gave Fitzgerald a chance to reduce the deficit once again, which he duly took.
Hanrahan took his tally to 14 points when he kicked another penalty early in the second half.
Despite Connacht scoring their first try when Carty was released down the blindside with ten minutes remaining, Munster held firm.
So its away interpros next up for against Ulster and Leinster before returning to the Sportsground for Champions Cup action against Toulouse on the 11th of January - Click here for tickets.
CONNACHT: Tiernan O’Halloran; John Porch, Tom Daly, Bundee Aki, Kyle Godwin; Conor Fitzgerald, Caolin Blade; Denis Buckley, Dave Heffernan, Finlay Bealham; Ultan Dillane, Quinn Roux (capt); Eoghan Masterson, Paul Boyle, Eoin McKeon.
Replacements: Stephen Fitzgerald for O’Halloran (55 mins), Shane Delahunt for Heffernan, Dominic Robertson-McCoy for Bealham (both 59), Jack Carty for C Fitzgerald (60), Robin Copeland for Masterson (61), Conor Kenny for Buckley (71), Joe Maksymiw for Roux (72), Stephen Kerins for Blade (73).