The first came in the 64th minute when CJ Stander latched onto a neat kick ahead by Ivan Dineen and the second was scored by replacement Mike Sherry in the right hand corner with four minutes of normal time to go.
The visitors who have played most of the rugby in the opening half, took the lead with a 9th minute Piers Francis penalty, before Munster, who were reduced to 14 with the 12th minute yellow card for BJ Botha, went in front thanks to Keatley penalties in the 21st and 27th minutes of a half that ended with Edinburgh on the offensive.
Munster: Denis Hurley; Johne Murphy, Ivan Dineen, JJ Hanrahan, Danny Barnes; Ian Keatley, Duncan Williams; Marcus Horan, Damien Varley, BJ Botha; Ian Nagle, Billy Holland; CJ Stander, Sean Dougall, James Coughlan capt. Replacements: Mike Sherry, Wian du Preez, John Ryan, Dave Foley, Tommy O'Donnell, Paddy Butler, Cathal Sheridan, Scott Deasy.
Edinburgh Rugby: Greig Tonks; Dougie Fife, Ben Cairns, Ben Atiga, Tom Brown; Piers Francis, Richie Rees; John Yapp, Andy Titterrell, Willem Nel; Perry Parker, Izak van der Westhuizen; Sean Cox capt, Stuart McInally, Netani Talei. Replacements: Steven Lawrie, Allen Jacobsen, Alex Allen, Grant Gilchrist, Hamish Watson, Chris Leck, Gregor Hunter, Lee Jones.