Five minutes later they extended that lead when Ciaran O'Boyle outstripped the Ulster defence after Tom Gleeson had made the hard yards.
Manning added a 33rd minute penalty before Richie McArthur opened Ulster's account with a similar score but when Manning added the extras to Coughlan's second try Munster looked comfortable.
However they lost Billy Holland to the sin bin in injury time and Ulster made hay with a try from impressive number 8 Chris Henry and McCarter's conversion left Ulster trailing by 12 points (22-10) at the break.
Ulster took their momentum into the second half and a Lewis Stevenson try converted by McCarter took them to within a score of the leaders and when Munster turned over ball on the half way line McCarter pounced and stretched his legs to score under the posts.
Leading 27-22 and with ten minutes remaining Ulster tried to close out the game but to their great credit Muster struck back. After they had been denied from a five metre line-out, Munster spread the ball wide for Conan Doyle to slice through to the left of the posts. Replacement out-half Eoghan Hickey tapped over the conversion to give his side a well deserved victory.
Munster: M Lawlor (D Hurley 55 min); C O'Boyle, T Gleeson, C Doyle, S Kelly; J Manning (E Hickey 60 mins), C Delooze (P.Rowley 60 min); E McGovern, A Kyriacou (S Cronin 47 min), T Ryan (R Feeney 70 min)); M Melbourne (M Essex 65 min ), C Wyatt; B Holland, A Kavanagh (D Sherry 65 min), J Coughlan.
Ulster: B Cunningham; M Kettyle, S Young, S Megaw (M McRae 39min), A Maxwell; R McCarter, P Marshall; N Conlan M Crockett, T Court; F Paulo, L Stevenson, R Caldwell, G Moore, C Henry.
Referee: David Keane.