The home side lost rising Tyrone star Rory Brennan to a straight red card after 24 minutes for striking Philip Smith, but were leading 1-5 to 0-5 thanks to McBrearty’s whirlwind start.
Ryan McHugh and McBrearty kicked early frees and then combined for the latter to shoot low across the goalkeeper and find the far corner in the sixth minute for the first goal.
Roscommon’s Colin Compton was Garda’s most dangerous forward and scored two of his 0-3 from play in the first half, at the end of which the visitors trailed by 1-7 to 0-5.
Garda, who had defeated Cork IT last week, struggled to contain Jordanstown’s superior firepower and Armagh’s Ethan Rafferty had a superb second half, scoring from play and long-range placed balls against the wind.
Seven minutes after the restart, Tyrone goalkeeper Sean Fox dived to his left to save a tamely hit penalty from Garda’s Daithí Shannon after Compton was fouled by Stephen Sheridan.
Mayo’s Evan Regan was denied a certain goal after a brilliant flying block by Gearóid Farren early in the second half.
However, he raised a green flag late on for UUJ, flicking home a 57th minute for the 2016 Sigerson Cup hosts.
Both sides finished with 14 players, with Carlow’s Brendan Murphy dismissed late on after picking up a black card to add to his earlier yellow.
P McBrearty 1-6 (5f), E Rafferty 0-4 (1f, 1 ‘45’), E Regan 1-0, K Clarke, M Argue, C Grugan 0-1 each, R McHugh 0-1 (f)
D Shannon 0-4 (4f), C Compton 0-3, P McGee, C Shields, B Murphy 0-1 each, G Haran 0-1 (f)
S Fox (Tyrone); R Johnston (Antrim), K Clarke (Cavan), R Brennan (Tyrone); R McHugh (Donegal), R McNamee (Tyrone), S Sheridan (Armagh); N McKeever (Antrim), M Argue (Cavan); C Grugan (Tyrone), E Rafferty (Armagh), D Savage (Down); E Regan (Mayo), R McAnespie (Monaghan), P McBrearty (Donegal)
F Burns (Tyrone) for Savage (40), C Clarke (Down) for Rafferty (58), S McArdle (Down) for Argue (59)
C Kenerick (Tipperary); G Farren (Donegal), G Petit (Roscommon), P Smith (Cavan); B Devlin (Louth), S O’Malley (Roscommon), BJ Molloy (Carlow); P McGee (Donegal), C Shields (Longford); P Morris (Cavan), B Murphy (Carlow), B O’Hare (Louth); C Compton (Roscommon), D Shannon (Cork), G Haran (Mayo)
M Holland (Roscommon) for McCarthy (HT), J Kerrigan (Galway) for O’Hare (40), P Fallon (Roscommon) for Devlin (53) J Kearney (Galway) for Molloy (58)
Padraig Hughes (Armagh)