Niall Cahalane's side enjoyed most of the possession until almost 10 minutes into the second period when Mary's three points down began to show more ambition.
The Cork side dominated the first-half and much of that can be put down to Dylan Mehigan at midfield, who reduced Down star Dan Gordon to a minor role.
However, the Belfast side's penchant for a two-man full-forward line and a 13-man defence when their opponents were in possession proved a stubborn obstacle. Pretty it wasn't.
Making both sides' jobs all the harder was the fact that the Sigerson Cup is being played under the old rules which on yesterday's evidence has less free-flowing football to offer than the new regulations.
The cynical obstruction of players off the ball while looking for a return pass reared its ugly head and for the most part Laois referee Eddie Whelan failed to give offenders a ticking.
But the old rules worked both ways.
Under the new instructions UCC's Fergal Griffin would have walked to the line after just 23 minutes.
UCC's concerns were of their own making though as they consistently took too much out of the ball. It took all of 15 minutes for the first score, from the boot of Cork senior Conor McCarthy. Sixty seconds later and UCC had the opportunity to blow the game wide open.
Cork senior panellist John Hayes was put through on the keeper after a stray pass from Mary's corner-back Cormac McAleer, but the UCC man's lob drifted wide.
Both sides were guilty of awful shooting but, gradually, the scores began to arrive with more regularity.
James Lavery got Mary's off the mark after 19 minutes but after another exchange of white flags UCC finally opened up the lead their possession if not their play deserved.
Unusually, it came from a trio of frees from different players, with Hayes, Fintan Goold and Hussey doing the honours. Twenty seconds after the break and the gap was four after the impressive full-forward Donncha Walsh slipped his marker.
Matters were getting serious for Mary's and they finally began to stretch their necks out with nothing left to lose. They clawed back the deficit as UCC stepped off the gas.
When Aidan McCarron landed a 48th-minute free for Mary's the gap was two but that was as close as they would come. For that, the Belfast outfit have only themselves to blame.
Just like UCC in the opening half, they were guilty of wasting some clear-cut chances.
The clincher arrived courtesy of the third of UCC's three Cork panellists in the half-forward line, Goold, with a long-distance effort. That left it 0-9 to 0-7 for UCC with less than three minutes to play and the best Mary's could manage after that was an exchange of points between McCarron and Kerry's Walsh.
UCC: D McInerney (Cork); D Óg O'Donovan (Cork), F Griffin (Kerry), N Donovan (Cork); G Burke (Tipperary), C O'Connell (Cork), J Wycherley (Cork); D Mehigan (Cork), P Kelly (Cork); F Goold (0-2, 1f, Cork), J Hayes (0-1, Cork), C McCarthy (0-1, Cork); R Hussey (0-4, 2f, Kerry), D Walsh (0-2, Kerry), L Ó Lionain (Waterford). Subs: C Brosnan (Cork) for Hayes 24, W Morgan (Cork) for Hussey 61, P Galvin (Kerry) for Kelly (63).
ST MARY'S, BELFAST: K Murray (Antrim); C McAleer (Tyrone), F Donnelly (Tyrone), T Hackett (Tyrone); T O'Neill (Antrim), J McMahon (Tyrone), M McIvor (0-1, Derry); D Gordon (Down), J Lavery (0-1, Armagh); L O'Hare (Armagh), L Meenan (0-2f, Tyrone), M Donnelly (0-1, Tyrone); D McCann (Armagh), A McCarron (0-2, 1f, Tyrone), G Smith (Armagh). Subs J Ball (Tyrone) for McMahon 10, P Quinn (Tyrone) for McCann 41.
Referee: E Whelan (Laois).