The Republic of Ireland international winger came off the bench in the 68th minute and replaced Nicky Butt.
Sam Allardyce: "Damien's a quality, top-drawer Premier League player.
Duff - Sam's 'New Player'!
"For me, it's like having a new player. He's worked exceptionally hard and got himself right up there.
"He got on the pitch, and didn't look out of place, I'm glad to say.
"It looks good for the future, and I hope he steers clear of injury."