Late bonus for Munster
Munster had laboured through a difficult first half but three scores after the break from CJ Stander, Duncan Casey and a 75th minute effort from Zebo got their European Cup campaign off to a solid start.
Treviso had almost shocked Munster at Thomond Park in the PRO12 earlier in the season and were in contention at half-time as they trailed the two-time winners by just three points.
But the Italian side had lost their previous 32 away games in Europe and after seven defeats from seven in the league this season, their challenge fell away in the second half.
Munster looked determined to make a quick start and took just four minutes to cross the whitewash.
Scrumhalf Conor Murray was among several Munster players held up just short of the line before South African World Cup winner BJ Botha crashed over from close range.
The tighthead prop, who put off retirement to sign a new six-month deal with the province this season, crossed for a second time after eight minutes but after going to the TMO he was shown to have lost control of the ball over the line.
Munster were in charge of the contest until Ian Keatley's clearance kick was charged down by Braam Steyn. The Treviso No.8 chipped ahead and grounded his own kick to bring the visitors level.
Keatley edged Munster back in front with a penalty after 19 minutes but it proved to be the last meaningful action of a poor first half that was dominated by the weather.
Handling errors from both sides littered the opening 40 minutes but with the wind at their backs in the second period Munster were hoping for better.
They got off to a decent start with a second Keatley penalty eight minutes after the interval but conditions were still making it difficult to put ball through the hands.
They finally got a breakthrough on 56 minutes when captain CJ Stander, who scored two against Treviso in the league earlier in the second, went over for their second try from close range.
Replacement hooker Duncan Casey got Munster's third try from a driving line-out with a little more than 10 minutes to go and the countdown was on to get the all-important fourth.
Munster's cause was helped when Treviso prop Matteo Muccignat saw yellow six minutes from the end after repeated infringements from the visitors.
A minute later, after going through the phases, Murray found wing Zebo out wide and he was left with a simple finish to wrap up the bonus point.
The scorers:
For Munster:
Tries: Botha, Stander, Casey, Zebo
Cons: Keatley 3
Pens: Keatley 2
For Treviso:
Try: Steyn
Con: Hayward
Teams:
Munster: 15 Andrew Conway, 14 Keith Earls, 13 Francis Saili, 12 Denis Hurley, 11 Simon Zebo, 10 Ian Keatley, 9 Conor Murray, 8 CJ Stander (captain), 7 Jack O'Donoghue, 6 Dave O'Callaghan, 5 Mark Chisholm, 4 Donnacha Ryan, 3 BJ Botha, 2 Mike Sherry, 1 Dave Kilcoyne.
Replacements: 16 Duncan Casey, 17 James Cronin, 18 John Ryan, 19 Dave Foley, 20 Robin Copeland, 21 Tomas O'Leary, 22 Rory Scannell, 23 Lucas Gonzalez Amorosino.
Treviso: 15 Luke McLean, 14 Ludovico Nitoglia, 13 Jayden Hayward, 12 Enrico Bacchin, 11 Tommaso Iannone, 10 James Ambrosini, 9 Edoardo Gori, 8 Abraham Steyn, 7 Alessandro Zanni (captain), 6 Francesco Minto, 5 Jean-François Montauriol, 4 Rudolph Duncan Naude, 3 Rupert Harden, 2 Ornel Gega, 1 Matteo Zanusso.
Replacements: 16 Davide Giazzon, 17 Matteo Muccignat, 18 Filippo Filippetto, 19 Dean Budd, 20 Marco Barbini, 21 Andrea De Marchi, 22 Chris Smylie, 23 Sam Christie.
Referee: Matthew Carley (England)
Assistant Referees: Tim Wigglesworth (England), Paul Dix (England)
TMO: Rowan Kitt (England)