The 34-year-old former Great Britain rugby league full-back - making his first union appearance for three years - struck in the 13th and 69th minutes to round off a heavy defeat for the competition's bottom side.
With the home flanker Matt Lacey in the sin bin for killing the ball, Munster scored two crucial tries in the opening four minutes of the second half, through Frankie Sheahan and Marcus Horan. Meanwhile, Ronan O'Gara rattled up a personal tally of 17 points with seven successful kicks.
Two penalties apiece from David Slemen and Paul Warwick saw Connacht trailing 13-12 at the interval, but their challenge soon faltered once they were playinginto a brisk breeze. After the break, the hooker Sheahan was driven over by a typical Munster maul and three minutes later Horan, a prop, outpaced the Connacht backs following a quick feed from his captain Anthony Foley.
Connolly, who previously played union for Harlequins (1996) and Orrell (2001-02), ran in his second try to seal a bonus point. Connacht claimed a late try via the wing Conor McPhillips, their only representative in the current Ireland international squad, but there was still time for the replacement prop Federico Pucciariello to score and complete Munster's 14th straight victory at the Sportsground.
In the day's other all-Irish Celtic League match, Leinster saw off Ulster 30-14 at Donnybrook. The Argentinian Felipe Contepomi kicked six penalties and one conversion for the home side, whose tries came from the back row forward Ciaran Potts and the Ireland wing Denis Hickie. Paddy Wallace and Neil Best went over for Ulster's tries, both converted by David Humphreys who was also on target with three penalties.
Harlequins opened up a one-point lead in National League One with a 27-7 home success over Doncaster. Bedford moved up to second with a 31-12 defeat of the third-placed Cornish Pirates.
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