Munster found a brave Treviso side tough to break down in the opening half, leading only 12-10 at the break - but moved up a gear in the second spell to earn a vital bonus point in front of 1,000 Munster fans who made the trip over.
Opposing centres Mike Mullins and Walter Pozzebon scored early tries, and former Ireland international Simon Mason gave the home side a surprise 10-7 lead with a simple penalty goal.
It didn't last long as skipper Jim Williams took a superb catch at the back of the lineout and hooker James Blaney was driven over. Ronan O'Gara was struggling with his kicking duties and the conversion went wide to give Munster a 12-10 lead at the break.
Mullins continued to be a thorn in Treviso's side and a stunning break after the restart should have resulted in Munster's third try, but the ball went to ground as the visitors' handling went from poor to atrocious.
One of the main culprits, inside centre Rob Henderson, made amends with a good break deep into enemy territory as Treviso's defence started to crack. Their cause wasn't helped when referee Joel Dume sent centre Manuel Dallan to the bin for a professional foul.
Munster took advantage of their one-man advantage with another drive over the try-line from a lineout - this time, Williams emerged from the pile of bodies with the ball.
The Irishmen scored a vital bonus-point try within minutes, with backrower and man of the match Anthony Foley celebrating his 57th Cup appearance with the five-pointer that puts Munster in the box seat in Pool 5.
The home side replied with a Franco Smith dropped goal, but yet another Mullins break set up replacement fullback Jeremy Staunton for Munster's fifth try.
Treviso were brave throughout and were rewarded in the final minute with a try to backrower Scott Palmer.
Final Score: Treviso 20 Munster 31
Man of the Match: Anthony Foley.
Munster (31) Tries: Blayney, Williams, Mullins, Foley, Staunton Cons: O'Gara 3
Treviso (20) Tries: Pozzebon, Palmer Con: Mason 2 Dg: Smith Pens: Mason
Shaun Payne; John Kelly, Mike Mullins, Rob Henderson, Anthony Horgan; Ronan O Gara, Peter Stringer; Gordon McIlwham, James Blaney, John Hayes; Donncha O Callaghan, Paul O Connell Jim Williams (Capt), David Wallace, Anthony Foley
Replacements: Frank Roche, Simon Kerr, David Pusey, Stephen Keogh, Eoin Reddan, Jeremy Staunton, Jason Holland.
Munster are still currently top of Pool 5 in the Heineken Cup with 19 points.