Substitute goalkeeper Kevin McLaughlin was the hero for the Donegal side after he saved two penalties to see the Inishowen League side progress to the first round.
Elsewhere, Intermediate Cup finalists Avondale United needed extra-time to progress past Newtown Rangers as David Shovlin scored a brace, as well as the decisive goal in extra-time, and last year's Intermediate Cup finalists Maynooth University Town are also through after a 5-1 win over Rockmount.
Glebe North, Malahide United and Collinstown also booked their place in the first round of the FAI Cup with two more qualifying round fixtures set to take place in due course.
FAI Senior Cup - Qualifying Round Results
Glebe North 2-1 Midleton
Newtown Rangers 3-4 Avondale United (AET)
Glengad United 1-1 Home Farm (4-3 pens)
UCC 0-2 Malahide United
Maynooth University Town 5-1 Rockmount
St. Mochta's 0-1 Collinstown
TBC: Lucan United v Aisling Annacotty, St. Michael's v Regional United
Byes: Cobh Wanderers, Crumlin United, Killester Donnycarney and Letterkenny Rovers.