Lowry popped up with the clock on 89 minutes to seal success by a single goal for Linfield in the first semi-final on a bumper day of Irish Cup football.
He converted with a back-post finish following Mark Haughey’s cross.
It handed Lowry a spot in the spotlight for the right reasons - having finished frustrated on 51 minutes when Swifts goalkeeper Andy Coleman produced a slick stop to block the Linfield man’s penalty.
Douglas Wilson felled Jamie Mulgrew in the box for the spot-kick shout.
In a goal-less first half, Wilson headed over after meeting a corner.
Dungannon’s best chance of the match came to substitute Peter McMahon in the 81st minute, but his deflected effort was brilliantly saved by Roy Carroll.
LINFIELD: Carroll, Stafford, Haughey, Callacher, Clarke, Lowry, Burns, Mulgrew, Quinn (Millar, 78), Smyth, Waterworth
Subs not used: Ward, Casement, Carson, Deane
DUNGANNON SWIFTS: Coleman, Burns, Hegarty, Armstrong, O’Rourke, Wilson, Harpur (Teggart, 89), Clucas, Glackin, Burke (McMahon, 56), Mitchell
Subs not used: Addis, Fitzpatrick, Lowe
Referee: Keith Kennedy (Lisburn)