The offer of bonus points for free scoring adventure was politely declined at Stevenson Park, where the emphasis was on prevention, containment and ultimately survival. The only try of the game was of the penalty variety, and in the end St Mary's prevailed due to an equally diverse combination of factors.
A superb second-half defensive performance, a touch of good fortune and an unusually disappointing return from the World Cup's most consistent goal kicker, David Humphreys, conspired to present Brent Pope with a most pleasing start to the campaign.
The St Mary's coach could not conceal his relief at Humphreys failure to convert a late penalty, his fourth miss from six attempts, which would almost certainly have given the Tyrone-men a win.
"We could not believe it when he missed that. They really did take the game to us in the second-half but they couldn't seem to get over the line when a try was going to swing the game," said Pope.
And he heaped praise on his side's heroic defensive effort, to which second-rows Higgins and Doyle made magnificent contribution. "Dungannon had all the ball in the second-half, and they lived near our line, but I was very pleased with our defence."
Dungannon coach Willie Anderson's worst fear was to some extent realised in the first-half when the absentee squad - nine were released from inter-pro duty for the first time last week - suffered from a lack of familiarity and failed to gel.
But it was a different story after the break, the home side really warming to the task and doing everything but put points on the board. "Overall I was very pleased with our performance, the players who came back in did gel very well," he said. "It was good to see Tony McWhirter and Paddy Johns playing so well. And even though he missed a couple of penalties, David Humphreys had a great game.
"He was outstanding in broken play, he created so many opportunities and it was he who got us into positions for those penalties.
"He made breaks, tackled and kept the ball on the move and kept varying the point of attack."
St Mary's broke the deadlock following a turgid opening 23 minutes when left wing John McWeeney was dragged back as he attempted to pounce on fullback Peter McKenna's kick ahead.
A penalty try was awarded, to which Mark McHugh added a conversion and a penalty. Humphreys opened Dungannon's account with a dropped goal, and as the newly promoted Tyrone-men peppered the visitors line after the break he kicked two penalties to leave just a point between the sides.
St Mary's, following a 20 minute bombardment, broke the siege with the help of the inspirational Victor Costello, but back came Dungannon again with Paddy Johns making an impressive return and Humphreys and Steven Bell linking well at halfback.
Humphreys, three minutes from the end, had a golden opportunity with a kickable penalty but his effort drifted wide and McHugh wrapped it up at the other end with an easy injury time kick.
Scoring sequence: 23 mins: St Mary's penalty try 0-5 M McHugh conversion 0-7; 27: McHugh pen 0-10; 40: D Humphreys penalty 3-10; 42: Humphreys penalty 6-10; 55: Humphreys penalty 9-10; 82: McHugh penalty 9-13.
Dungannon: M Bradley; J Davis, J Cunningham, A Clarke, T Howe; D Humphreys, S Bell; J Fitzpatrick, A Clarke, G Leslie, P Johns, K Walker, J Patterson, A Hughes, T McWhirter.
St Mary's: P McKenna; D Hickey, M McHugh, G Gannon, J McWeeney; F Campion, P Lynch, E Byrne; P Smyth, P Coyle, I Bloomer, M O'Kelly, P HIggins, Higgins R Doyle, V Costello. Replacement: M Foxe for Byrne.
Referee: R McDowell (Ulster)