Dan McFarland’s side had started the day in second place - but with the Stormers getting a bonus point win over Glasgow coupled with Munster’s 24-17 victory in Belfast, Ulster have slipped to fourth in the table.
The top four will get home advantage in the quarter-finals and Ulster could end the weekend in fifth if the Sharks beat Leinster with a bonus point this afternoon.
Ulster showed no signs of a hangover from their European exit at the hands of Toulouse as scrum half John Cooney nudged his team in front with a seventh-minute penalty after Munster lock Jean Kleyn was punished for a high tackle in midfield.
But that would prove to be the home side’s only return in the first half.
Munster out half Joey Carbery tied the scores on 11 minutes with a penalty from in from off the posts after a high tackle by Michael Lowry.
Munster got the game’s opening try on 21 minutes.
The visitors kicked a penalty to the corner, the lineout wasn’t perfect but Jack O’Donoghue gathered and drove to the line.
He was stopped then, after another couple of probes by the forwards, tight head prop Stephen Archer rumbled over with Carbery converting.
Munster cut Ulster open on 27 minutes, Kleyn and Jason Jenkins carried making hard yards, Damian De Allende injected pace into the attack creating an overlap, he quickly fed Carbery, the out half found Chris Farrell, the former Ulster centre stood up Stewart Moore before shipping the ball to winger Keith Earls for an easy run-in.
But Carbery was off target with the conversion.
Ulster finished the half strongly but failed to turn possession and territory into points, allowing Munster to go into the interval with a 15-3 lead.
Carbery extended Munster’s lead three minutes after the restart with a penalty after Jordi Murphy took a man out off the ball.
Ulster got back into the game with their tried-and-tested maul on 48 minutes.
Lowry found touch from a penalty, the forwards set up a drive off the lineout and hooker Rob Herring broke off the back from the maul to touch down with Cooney converting.
Ulster wasted a great opportunity on 55 minutes when from an attacking line out on the Munster five-metre line they conceded a needless penalty, allowing the visitors to clear their lines.
Ulster replacement prop Gareth Milasinovich was guilty of not releasing the ball in the tackle, allowing Carbery to land a long-range penalty on 59 minutes.
Munster winger Shane Daly was yellow-carded on 73 minutes for deliberately kicking the ball out of the ruck and Ulster took immediate advantage.
The penalty was kicked to the corner, Brad Roberts peeled off the maul and surged for the line but he was stopped.
Nathan Doak hit Sean Reidy and the flanker dived over a pile of bodies to claim the try.
Doak landed the conversion to close the gap to four points.
Carbery landed a last-minute penalty after Ulster were punished for jumping across the lineout.
Munster were able to field Madigan’s short restart, the forwards drove and forced a penalty to close out the game.
Ulster: S Moore, R Baloucoune, J Hume, S McCloskey, E McIlroy, M Lowry, J Cooney, A Warwick, R Herring, M Moore, A O’Connor, I Henderson, M Rea, J Murphy, N Timoney,
Replacements: B Roberts (for Herring, 59 mins), E O’Sullivan (for Warwick, 64 mins), G Milasinovich (for Moore, 23 mins), S Carter (for Henderson, 41 mins), S Reidy (for Rea, 61 mins), N Doak (for Cooney, 51 mins), I Madigan (for S Moore, 70 mins), B Moxham
Munster: M Haley, K Earls, C Farrell D de Allende, S Daly, J Carbery, 9. C Casey, J Loughman, D Barron, S Archer, J Kleyn, J Jenkins, J O’Donoghue, J Hodnett, A Kendellen.
Replacements: S Buckley (for Cloete, 65 mins), J Wycherley (for Loughman, 52 mins), J Ryan (for Archer, 51 mins), T Ahern (for Jenkins, 52 mins), F Wycherley (for Kleyn, 59 mins), C Murray (for Casey, 64 mins), B Healy, C Cloete (for Hodnett, 64 mins).
Referee: J Peyper (South Africa)