The games only goal was scored in the 10th minute by Keith Cowan from a Michael Funston cross.
On 26 minutes Funston was then shown a red card for a tussle with a Rovers player while Sean Mc Carron also headed for the showers in the second half after two yellows.
With around 15 minutes to go Harps boss Ollie Horgan was also sent off. He was not happy with a challenge by Rovers Evan Osam and after some strong words with the fourth official Horgan went to the stands.
Keeper Conor Wynn had a great game for the Donegal side in shutting out Rovers late in the second half.
Harps held on for the victory and their second win at the Tallaght Stadium this season.