Connacht were seconds away from a first win over Munster in 18 seasons but Paul Burke's late penalty secured the home side a 27-27 draw at Musgrave Park.
Munster (24) 27:
Tries: Horgan, Leamy, Payne, Cullen.
Cons: Burke 2.
Connacht (14) 27:
Tries: O'Brien, McPhillips, Clarke.
Cons: Warwick 3.
Pens: Warwick 2.
Munster led 24-14 at half-time but Adrian Clarke's try and some good kicking by Paul Warwick put Connacht into the lead in the closing stages.
Anthony Horgan, Denis Leamy, Shaun Payne and Christian Cullen scored first half tries for Munster.
Niall O'Brien and Conor McPhillips also scored Connacht tries.
The visitors, buoyed by last Saturday's 31-15 turnover of Glasgow, went in front on 11 minutes, as summer signing O'Brien was put over after centre partner
Matt Mostyn had produced a clever dummy run to expose Jason Holland.
Paul Warwick converted but saw his restart clearance charged down by Munster scrum-half Mike Prendergast, and the home side built the phases for Horgan to score in the left corner four minutes later.
Leamy's try then came after the flanker had bulldozed through both Ted Robinson and Tom
Tierney, to stretch over in the corner on 21 minutes.
Touch judge Tony Redmond then sin-binned Munster tight head prop Gordon McIlwham for throwing a punch in a ruck.
Christian Cullen scored a try but also gifted Connacht a touchdown
However, Munster still managed to pull 17-7 ahead with Leamy breaking clear over halfway with turnover ball and South African Payne finished off the move
in the same left corner.
Cullen then made a blunder, losing his own tap ball on the Munster '22 for McPhillips to bring Connacht back within three.
However, the classy side of the New Zealander was evident in first half injury-time when the full-back touched down under the posts to help increase Munster's lead to 24-14.
Warwick energised the men in green with a penalty seven minutes into the second half and Connacht were back level by the 55th minute.
Another brutish maul forward reduced Munster's front eight to a bit part and 30-year-old prop Clarke
was driven over.
Trevor Hogan felt the wrath of Welsh referee Nigel Owens with 15 minutes remaining and, with the Munster lock sin-binned, his bringing down of the
lineout saw Warwick kick Connacht 27-24 in front.
With the reassuring hands and boot of veteran Eric Elwood on the field for a bloodied David Slemen, Connacht looked resolute in defence.
However, Elwood's Irish out-half rival of the mid-1990s, Burke had the last laugh as his injury time penalty
ended the visitors' hopes of going top of the Celtic League.
Munster: C Cullen; J Kelly; S Payne, J Holland, A Horgan; P Burke, M Prendergast; F Roche, J Flannery, G McIlwham, S O'Connor, T Hogan, S Keogh, D Leamy, J Williams, capt.
Replacements: J Blaney, E McGovern, D Ryan, J O'Connor, E Reddan, J Storey, R Henderson.
Connacht: D Slemen; T Robinson, M Mostyn, N O'Brien, C McPhillips; P Warwick, T Tierney; A Clarke, J Fogarty, P Bracken, C Short, A Farley, J Muldoon, M Lacey, J O'Sullivan.
Replacements: Henry Bourke, Stephen Knoop, Michael Carroll, Paul Neville, Conor O'Loughlin, Eric Elwood, J Meagher.
Referee: Nigel Owens (WRU).