His opener came on 27 minutes after a shot by the influential Julio Arca had been spilled into his path.
The visitors equalised against the run of play, Richard Cresswell winning a penalty that Graham Alexander scored.
But Sunderland deservedly claimed the points thanks to a goal by Darren Carter on his debut and another tidy finish by Elliott on 52 minutes.
Preston caretaker boss Billy Davies:
"I have been asked to do the job and will just take each game as it comes.
"I have to work with the players I have and we all have a job to do - it's
the board who make decisions.
"We've got a small squad and have lost some key players through injury.
"But you can't come to a place like Sunderland and have so many players not on
top of their game."
Sunderland: Poom, McCartney, Breen, Stephen Caldwell, Wright,
Arca, Robinson (Lawrence 65), Carter, Whitehead,
Elliott (Johnson 90), Stewart.
Subs Not Used: Oster, Lynch, Myhre.
Booked: Arca, Stephen Caldwell.
Goals: Elliott 27, Carter 45, Elliott 52.
Preston: Lonergan, Curtis, Lucketti (Davidson 45), Mawene,
Alexander, Lewis, O'Neil, Etuhu, Skora (Smith 68), Cresswell,
Healy (Lynch 69).
Subs Not Used: McCormack, Ward.
Goals: Alexander 39 pen.
Ref: A Kaye (W Yorkshire).