Two successful Staunton penalties early on had Munsters 6-0 in front.
But, in one of their rare incursions inside the Young Munster 22, Cork Con’s Niall O’Driscoll nipped in for his sixth try of the season which out-half Johnny Holland converted.
An early second-half penalty by Staunton proved to be the match-winning score, although Munsters were left hanging on as Holland sent a last-gasp drop-goal wide of the target.
Munsters are now just four points behind leaders St Mary’s in third, while fifth-placed Con are 11 points behind.
Clontarf are also bearing down on Mary’s, two points adrift in second place, after they saw off Dolphin 32-23 at Castle Avenue, exacting revenge for a 9-3 turnover in Cork last month.
Hooker Turlough Considine claimed a brace of tries with Michael McGrath and Simon Crawford notching the others, while Richie Lane’s three conversions and two penalties took his seasonal points tally to 106.
Dolphin got back into losing bonus point territory with a penalty try and two well-taken efforts from influential number eight Ryan Murphy, but Clontarf’s attacking prowess was too much for them.
Mary’s were thankful they did enough in the first half to see off Garryowen 13-12. Jonathan Sexton’s brother Mark scored the game’s only try with Ray Crotty kicking the rest.
Declan Cusack’s four penalties had the light blues within touching distance as they kept the hosts scoreless after the break, but Mary’s held on to claim their eighth league victory on the trot.
Tadhg Bennett’s 17-point haul proved decisive on the Aviva Stadium’s back pitch, as he gave Shannon a vital four points with a 22-17 win over Lansdowne, despite the Dubliners outscoring Shannon three tries to one.
Blackrock College got the better of fellow strugglers Old Belvedere 18-11 in a hard-fought game at Stradbrook.
Darragh Fitzpatrick was again Rock’s key contributor, the out-half claiming a converted try and two penalties to give his side a seven-point buffer over their local rivals, who prop up the table.
Meanwhile, with Ballynahinch and Dungannon drawing 22-22 on Friday night, Belfast Harlequins’ 19-13 home victory over Galwegians has put them top of Division 1B. Scrum-half Ian Porter again did the damage for them, converting a penalty try and kicking the remainder of their points.
At Eaton Park, home advantage helped Ballymena see off Bruff on a 17-8 scoreline and move up to third.
Centre David Lynch’s two tries had UCD 12-0 up against Buccaneers, but the visitors came good after the break with an Alex Hayman try and 11 points from out-half Jack Carty.
Neither UL Bohemians or UCC could manage a first half score in this afternoon’s mudfest at Annacotty, but the dominant UL pack got on top in the second half to carve out a 8-3 victory.