Former Great Britain rugby league full-back Gary Connelly celebrated his return to the 15-man game with two tries for Munster while Frankie Sheahan, Marcus Horan and Federico Pucciariello also crossed the whitewash.
Fly-half Ronan O’Gara added 17-points with the boot to severely punish the homeside.
Two penalties each from David Slemen and Paul Warwick saw Connacht trailing 13-12 at the break but, turning around into a brisk breeze, their challenge faltered.
David Slemen’s penalty in the second minute gave Connacht some reward from a bright opening start, however Munster hit back as Connolly took a lovely inside pass from Ian Dowling for a converted try.
Slemen grabbed a second penalty before injury forced him off but his replacement Paul Warwick slotted a huge effort to give the home side a 9-7 lead on the half hour.
Warwick and O’Gara cancelled each other out with a penalty before O’Gara put Munster ahead after flanker Matt Lacey was yellow carded for killing the ball in first half injury-time.
Munster put the pressure on from the start of the second half after lock Donncha O’Callaghan took a fine lineout to set up a maul with hooker Sheahan finishing it off with his try.
Three minutes later prop Horan showed some surprising pace after he was fed by Anthony Foley and raced down the right flank to score. Once again O’Gara converted.
Munster were down to 14 men after skipper Foley was sinbinned, however that did not stop the visitors who grabbed their fourth try and a bonus point when Connolly went over for his second.
Winger Conor McPhillips grabbed one back for Connacht but the last word went to Munster as substitute prop Pucciariello rubbed salt in Connacht’s wound.