Munster produced all the early pressure and Mick O'Driscoll looked certain to score a try as he drove at the Ulster line but he spilled possession and allowed BJ Botha to gather.
Ulster's first foray into Munster territory in the 11th minute yielded an immediate three points as Ian Humphreys slotted a penalty following a James Coughlan infringement.
Ulster's Tom Court was winning his battle in the scrums with another Irish international Tony Buckley as the visitors were struggling with the set-piece.
Warwick gifted Ulster their opening try as the Munster fly-half's attempted chip to Doug Howlett was blocked by Paddy Wallace with Danielli grabbing possession and running in unopposed in the corner.
Humphreys added the conversion and four minutes later Danielli scored again in the same corner after Trimble had ghosted past de Villiers in midfield before passing to the Scottish winger.
Munster's back-row concerns, with Denis Leamy already out injured for a protracted period, increased when Neil Ronan was forced off by injury in the 25th minute.
Jean de Villiers tries to break away from Ulster's Tom Court at Ravenhill
The visitors badly needed the next score to get back into the game and it came after a sustained period of pressure.
Coughlan had been held up just short of the Ulster line and Munster were also frustrated as the gamble of opting for two line-outs instead of slotting easy penalties failed to yield a score.
However, Munster did open their account in the 34th minute as de Villiers ran in under the posts after Humphreys had failed to hold on to possession following a turnover.
Warwick slotted the conversion and he added three further points before the break to cut Ulster's lead to 15-10.
Munster nearly gifted Ulster a try in the 48th minute as Wallace was adjudged to have knocked-on inches short of the line after Paul Warwick and Denis Hurley had got into a muddle following a wayward Peter Stringer pass.
However, the match became bogged down in an attritional struggle during the remainder of the third quarter as neither side managed a score.
Warwick hit the woodwork from 40 metres with 15 minutes left while Munster wasted an overlap chance from the follow-up after replacement Thomas Anderson's knock-on.
However, the game was largely played in the middle third of the field for the majority of the second half.
Munster produced late pressure but were unable to fashion another score as they had to be content with a losing bonus-point.
Ulster coach Brian McLaughlin: "We started quite well, getting a turnover try and then Simon Danielli completed a nice move. We were very pleased at that stage.
"As the game went on it got uglier and uglier and I'm delighted we hung on and got the points.
"We defended well at times around the pitch. We were rugged in the last 10 minutes with our defence excellent.
"There were a lot of pluses but it was not an ideal performance by any means."
Ulster: J Smith, A Trimble, I Whitten, P Wallace, S Danielli, I Humphreys, I Boss, T Court, N Brady, BJ Botha, E O'Donoghue, D Tuohy, S Ferris, W Faloon, C Henry (capt). Replacements: Nagusa for Wallace (52), O'Connor for Humphreys (61), Kyriacou for Brady (55), Anderson for Henry (4). Not used: D. Fitzpatrick, Caldwell, Willis.
Munster: D Hurley; D Howlett, L Mafi, J de Villiers, I Dowling; P Warwick, P Stringer; W du Preez, D Varley,T Buckley; M O'Driscoll, D Ryan; B Holland, N Ronan, J Coughlan. Replacements: Archer for Buckley (70), O'Donnell for Ronan (25), O'Mahnoy for Coughlan (70). Not used: Sherry, D. Williams, Deasy, Gleeson.
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