McVeigh struck in the 75th minute to give the locals lads hope of landing a dream FAI cup final date at the Aviva.
The goal sparked huge celebrations at Leckview after a very tense game with sides evenly matched.
But substitute David Shovlin scored the second goal in injury time to seal the tie and that dream trip to Dublin.
There were huge celebrations at Leckview as the final whistle went with a crowd of more than 500 watching the game.
Ringmahon had the early chances but were stopped in their tracks by goalkeeper Ruairi Kelly in fine form for Rovers.
The sides went in level at the break but the Eamon McConigley’s team gradually began to find the openings.
The central defensive pairing of Shane Bradley and Paul Boyle stood resolute in the second half especially after the two goals and Ringmahon just couldn’t find a way through.
Mark Forker continued to pull the string in the middle of the park as the evergreen Terence Shiels seems to be getting fitter as he gets older with a super display.
Darren McElwaine continued to sniff out any openings that came his way while McVeigh was always a threat down the left flank.
The Donegal outfit were fully value for their victory and a date in the Aviva Stadium on May 14th next is nothing less than they deserve.