Both sides lost players in the 26th minute when Mickey Funston and Ryan Doolin became involved in an off-the-ball incident and were shown red cards.
Harps had been leading from as early as the tenth minute when a Funston corner was played short for Josh Mailey who squared to Keith Cowan who found the net.
It was a great start for the Donegal side but they had to call on goalkeeper Conor Wynn time and time again.
Harps battled hard to forge the openings and went in ahead at the break.
Ollie Horgan’s side were reduced to nine men in the 68th minute when a rush of blood to the head saw Sean McCarron receive his marching orders.
McCarron had received a yellow two minutes earlier but when he blatantly took down Onwubiko, the ref had no choice but to send him for an early shower.
From then on Harps tried to batton down the hatches and they were helped by a confident display by ‘keeper Wynn.
The big Galway man puled off a superb save in the 72nd minute to prevent a Zack Watson goal-bound effort.
Harps manager Ollie Organ found himself in the stands when he was given his marching orders for remonstrating with the ref.
Harps managed to hold on and will be delighted to record their second victory at Tallaght stadium this season.