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Tries in either half from Tiernan O’Halloran and Man of the Match Bundee Aki were added to by the boot of inside centre Craig Ronaldson who kicked eight points.
Munster also scored both sides of the break with hooker Niall Scannell touching down from a rolling maul after 20 minutes while a controversial penalty try was awarded following the sin binning of captain John Muldoon for an early tackle.
Despite being reduced to 14 men, the visitors regrouped and dug deep in defence to hold out a determined Munster side. Aki’s unconverted try after 77 minutes extended the lead to six points and Connacht held out for an important win in Limerick.