Gary Liggett scored both goals as Dungannon Swifts moved further away from the relegation zone thanks to their second away win in five days.
Having taken three points at Coleraine on Friday, the Swifts took an 18th-minute lead at Drumahoe when Liggett headed in from Matt Hazley's corner.
Dungannon's lead was doubled on 29 minutes when Liggett volleyed in a fine shot from about 15 yards.
Robbie Hume shot in from a tight angle for Institute in the 56th minute.
The North-West club, three points adrift at the foot of the Premiership table, pushed for an equaliser and went close when defender Graham Crown's header struck the underside of the crossbar.
Home substitute Michael McCrudden fired a shot narrowly wide and then forced a fine save from Swifts keeper Andy Coleman.
Darren Murphy's Dungannon are now seven points ahead of Institute and four better off than one-from-bottom Warrenpoint Town.
In the end, Institute's valiant fight back in the second half fell short and they are in danger of making an immediate return to the Championship.
Dungannon bossed the first period and were well worth their two-goal interval advantage.
Liggett got the opener with a close-range header from Hazley's corner.
His second goal was a fine finish as he controlled a high ball into the area with his first touch, and volleyed a superb shot past keeper Fergal Murphy with his second.
Institute showed more threat in the second half and had Dungannon on the back foot.
However, they only scored once through Hume early in the second half and that meant Paul Kee's strugglers fell to a fourth successive league defeat.
Dungannon manager Darren Murphy: "We definitely won ugly tonight and I felt Institute were exceptional in the second half.
"I think it was the best second-half display by any team against my side this season.
"They created chances but only took one of them. My back five defended resolutely and the keeper made a few good saves when he had to."
Institute manager Paul Kee: "I am bitterly disappointed with our display in the first half.
"If we continue playing like that we will not be catching anybody.
"We have to learn, and learn fast."