A Gavin Dunne penalty on the stroke of half-time was the only score of a cagey opening half dominated by defences and a swirling rain.
Dolphin took control after the interval when centre John Gleeson burst through and out-half Rory Scannell converted to put the visitors 7-3 ahead.
But quick tries from winger Darren Hudson and hooker Dylan Fawsitt with seven further points from the boot of Dunne turned the tide in the Dubliners' favour.
St. Mary's were looking to bounce back from a 25-6 loss to Clontarf last weekend which was the Dublin club's first reversal in five matches.
Dolphin, in stark contrast, had leaked an alarming 114 points in two games and came into this fixture with the league's worst defensive record.
They did, however, come out on top in the previous meeting between the two sides back in October, when the Musgrave Park outfit won 15-10.
But with Schmidt watching on just seven days after his side's own heroics in Paris, both teams were eager to impress and started the contest at a high tempo.
Scoring opportunities were limited as each team nullified the other's attacks in the swirling rain, which forced the floodlights to be switched on.
The game's first major incident came in the 28th minute when St. Mary's prop Colm McMahon was sin-binned for infringing. Scannell, who earlier missed a drop goal attempt, kicked his penalty effort wide.
Despite being a man down, the home side matched their Munster opponents and had Steve Toal-Lennon's pass reached its intended target, they would have scored the game's first try.
The game's opening score did arrive in the final play of the half as St. Mary's, restored to 15 players, took the lead from Dunne's converted penalty on the 22.
After the restart the match came to life when Eoin O'Shaughnessy's sublime pass off a lineout sent Gleeson clean through on 54 minutes. Scannell's extras put Dolphin 7-3 ahead.
St. Mary's though clawed three points back immediately from the boot of Dunne and then turned the tie on its head with two tries in a matter of minutes.
The first of them came in the 64th minute as the home side regained the lead through Hudson's converted try in the corner.
And then just three minutes later, they increased their advantage when Fawsitt pounced on some loose back-line passing from Dolphin in defence to go over.
A fourth successful kick by Dunne put the hosts out of sight at 20-7 as the game was played out to its inevitable conclusion.
Clontarf, who have a game in hand, closed the gap on leaders Old Belvedere to three points as they ran out 32-12 winners over lowly Garryowen at Dooradoyle.
Former Ireland Under-20 hooker Bryan Byrne had a day to remember with a hat-trick of tries - his haul showing how dominant Clontarf were in the forward exchanges and the maul - while winger Michael McGrath grabbed the other try.
David Joyce had a early chance for the north Dubliners but his penalty drifted wide, and opposite number Andrew O'Byrne was also off the mark with a Garryowen penalty.
Hopes that the revival for the Limerick club would continue were raised when they went in front with a try after 21 minutes by winger Alan Gaughan which O'Byrne converted.
That was as good as it got for the home side in the first half as Clontarf stepped up the pace and by half-time they had the points in safe keeping when they led 22-7.
The visitors had the bonus point wrapped up after 62 minutes and a late try by Shane Buckley, who lined out in the second row for Garryowen, only salvaged some pride for the well-beaten Light Blues.
Lansdowne got a rare opportunity to play on the main pitch at the Aviva Stadium, but the result did not go their way as Cork Constitution claimed the spoils on a 24-18 scoreline.
Tom Mulcahy's side finished strongly with a 10-point burst, including a 70th minute try from replacement full-back Chris Quinn and a late penalty from stand-in captain Darragh Lyons.
Cork Con had started the game in fine fashion, impressive back rower James Ryan breaking through for an eighth minute try which was cancelled out by Lansdowne winger Foster Horan eight minutes later.
Tom Daly booted Lansdowne into a 13-7 lead but they lost their captain Willie Earle and tighthead prop Adam Boland to the sin-bin before half-time.
Constitution forced the issue in the scrum, with current Ireland Under-20 hooker Max Abbott showing well, and they registered a penalty try to take a one-point lead into the second period.
Lansdowne exerted the early pressure on the resumption and it eventually paid off when industrious back rower Charlie Butterworth crossed the whitewash in the 57th minute.
However, Cork Con had the better of the final quarter as they leapfrogged over Lansdowne into third place in the table.
Ballynahinch claimed only their third victory of the campaign as they powered past Young Munster, running in five tries for a 36-3 success at Ballymacarn Park.
Rodger McBurney and Ulster's David McIlwaine scored a brace of tries apiece, with replacement James McBriar also touching down for Derek Suffern's side.
The result has moved 'Hinch five points clear of bottom side Garryowen at the foot of the table, as the battle to avoid automatic relegation intensifies.
Leinster back rower Jack Conan, who was the Division 1A Rising Star for January, touched down in Old Belvedere's 19-8 victory over neighbours UCD at Anglesea Road.
'Belvo's fourth March win was confirmed by two second half penalties from goal-kicking winger Josh Glynn after 57 and 66 minutes, as they overcame a UCD side that put 55 points on Dolphin last Sunday.
First half tries from winger Philip O'Dwyer and number 8 Conan had sandwiched Emmet MacMahon's 17th-minute effort for the students.
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