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Man-of-the-match Ian Humphreys also enhanced his chances of featuring in Ireland's RBS 6 Nations squad as he orchestrated many of Ulster's key scores, while contributing 12 points of his own.
Nothing went right for Munster with knock-ons and poor decision making undermining their play while Ronan O'Gara and Rua Tipoki both limped off with injuries.
Ulster looked cohesive right from the kick-off, working through the phases and threatening out wide through Timoci Nagusa and the deceptively quick Cave.
The returning Tipoki, playing for the first time since sustaining ligament damage against New Zealand, showed some neat touches as Munster marched back downfield.
But when an O'Gara grubber kick was blocked down on the Ulster 22, the visitors quickly turned possession into a breakaway try.
Stephen Ferris did well to gather the loose ball and find Nigel Brady and although the hooker's pass on the 10-metre line to Wallace looked decidedly forward, referee Alan Lewis allowed play to continue and the Ulster centre had the legs on the Munster cover to go in under the posts.
Humphreys tapped over the conversion and Munster were struggling to get out of first gear, with O'Gara pushing a penalty attempt wide before he departed with a hamstring injury.
Humphreys moved Ulster 10-0 ahead but O'Gara's replacement Paul Warwick converted a 20th-minute penalty to get Munster on the scoreboard.
Munster gained territory through Warwick's line kicking, however Matt Williams' men were solid in the lineout and showed more commitment at the breakdown.
And then, nine minutes from the break, Humphreys' well-weighted kick out to the left bounced perfectly for the onrushing Cave to slip through for a sucker-punch try.
Humphreys increased his influence by nailing the conversion from the touchline, before Warwick replied with a penalty.
But Ulster pressed for more points and their adventure was rewarded in first half injury-time when Humphreys brilliantly off-loaded for replacement McCrea to stretch his legs and crash over in the right corner.
Munster were 22-6 down at half-time and the sight of Tipoki limping off only served to add to their woes.
It took Ulster just six minutes after the interval to get their bonus point score when prop Court burrowed over for a converted try.
Federico Pucciariello and Matt McCullough saw yellow for an off-the-ball clash and Ulster were down to 13 players when stand-in captain Kieron Dawson was sin-binned for a deliberate offside.
Before that, Humphreys had managed to tag on another penalty and while Munster gained some consolation with a Warwick-inspired try for Howlett, Ulster's defending was typified for the efforts of Ferris and Paul Steinmetz in denying Kieran Lewis a certain try.
With mistakes littering their game, Munster coughed up another try five minutes from time when Trimble dotted down after following up on a dinked kick from Humphreys.