Paul Warwick added the difficult conversion but Connacht were never to going to let this one slip easily.
They struck back with a George Naoupu try in the 59th minute after Munster could have closed it out when they laid siege to the Connacht line minutes earlier.
In those closing frantic minutes Munster held their nerve and just as impressively laid bodies on the line for a win that leaves them third place in the table on 43 points, the sameas Ospreys who they play next Saturday.
Playing with a strong breeze Munster first on the scorboard with a Paul Warwick penalty after just three minutes and he extended that lead six minutes later with another successful penalty.
Connacht took the lead with a 12th minute Johnny O'Connor try converted by Ian Keatley, a score that originated with a clear knock-on by Fionn Carr as he tried to gather a Garryowen on the Connacht 22.
In the 30th minute, Nick Williams made a clean break that was carried on by Tony Buckley and when Munster went right Warwick delivered the scoring pass to Ronan.
Munster: Scott Deasy; Danny Barnes, Tom Gleeson, Paul Warwick, Simon Zebo; Declan Cusack, Peter Stringer; Dave Ryan, Damien Varley, Tony Buckley; Mick O'Driscoll capt; Billy Holland; Nick Williams, Niall Ronan, James Coughlan. Replacements: Denis Fogarty, Julien Brugnaut, Dave Foley, Peter O'Mahoney, Conor Murray, Jeremy Manning, Sean Scanlon.
Connacht: Gavin Duffy, Troy Nathan, Niva Ta'auso, Keith Matthews, Fionn Car, Ian Keatley, Frank Murphy, Brett Wilkinson, Sean Cronin, Jamie Hagan, Michael Swift, Bernie Upton, John Muldoon capt., Johnny O'Connor, George Naoupu. Replacements: Adrian Flavin, Ronan Loughney, Michael McCarthy, Mike McComish, Conor O'Loughlin, Miah Nikora, Aidan Wynne.
Referee: Alain Rolland.