Replacements used: Arthur Lyons for Bradshaw (23-25 mins, temp sub), Kevin Croke for Bradshaw (51), Lyons for McMahon (56), Andrew Burke for O'Driscoll (65).
Replacements used: Patrick Galvin for Cagney (43-45, temporary sub), Cathal O'Flaherty for O'Meara, Galvin for Cagney (both 51), Brian Vaughan for A O'Driscoll (80+4).
The three-pointer came just after Constitution narrowly missed out on scoring the first try of the contest courtesy of a fine drive from their scrum.
But the power of their pack, which included Munster's Ian Nagle and John Ryan, eventually paid dividends. A terrific spell of pressure to the right of the posts led to referee John Lacey awarding them a 13th minute penalty try.
Holland tapped over the simple conversion for a 10-0 lead. St. Mary's had enjoyed a good deal of possession during the opening quarter hour, but they were finding it difficult to break through a tight and compact Constitution back-line.
The hosts opened their account after 17 minutes when out-half Gavin Dunne, who returned to the side in place of Steve Toal-Lennon, found the target with a close range penalty.
This was quickly cancelled out by a second Holland penalty on the 20-minute mark, but St. Mary's forced Cork Con into the concession of another penalty and Dunne slotted over with confidence.
Slowly but surely, St. Mary's were settling into proceedings. They had an opportunity to reduce the gap even further with a 40th minute penalty, but Dunne's kick went wide and left the Leesiders 13-6 ahead at the interval.
With the conditions becoming more difficult as the game progressed, it came as no surprise that the play from both teams was somewhat scrappy after the restart.
Cork Con were still controlling the game for the most part though, and they restored their 10-point advantage thanks to Holland's third penalty of the afternoon.
The influential out-half also had place-kick opportunities from long range in the 58th and 62nd minutes respectively but, much to the relief of the home support, he felt short with these kicks.
This was certainly a let-off for St. Mary's. Hugh Hogan's charges took full advantage by grabbing their first and only try with 15 minutes remaining.
Wily scrum half Matthew D'Arcy was the man who crossed the whitewash for the hosts. His try under the posts ensured that Dunne had an easy conversion.
St. Mary's had now brought the deficit down to three points, setting up a tantalising finale as these top flight heavyweights slugged it out.
Even though the frantic nature of the action led to yellow cards being issued to St. Mary's number 8 Darragh Keller and Cork Con flanker Graeme Lawler, two late penalties from scrum half Gerry Hurley secured the four match points for Brian Walsh's men.
Referee: John Lacey (IRFU)