Ulster were quick to respond with a try and conversion from Ian Humphreys after 19 minutes bringing the scores level, 7-7.
Ulster went ahead with a converted penalty from Humphreys, but Munster continued to attack and their patience paid off after several phases when David Wallace, supported by the pack, made it over the line for Munster's 2nd try.
Munster led14-10 going in at the break.
Munster opened up their lead and went on to score two further tries in the closing half, Earls touching down on the wing after 46 minutes and Warwick scoring the bonus winning try in the closing minute of the game.
Captain Paul O'Connell after the game "We really needed to improve tonight and show that we could do it, we needed a big performance at home and in front of our own supporters."
Tony McGahan commented "We really needed to match the Ulster physicality at the breakdown and throughout the phases, and I think we did that tonight. Young Stephen Archer did really well tonight, and Denis Fogarty did very well up front and throughout the set pieces."