The 27-year-old played a neat one-two before bursting into the box and side-footing low into the far corner.
Brett Ormerod should have equalised from the penalty spot but his weak effort was saved by Mart Poom.
Chris Brown's flick went narrowly wide and Briane Deane had a headed effort ruled out in a poor first half but the Black Cats dominated after the break.
Sunderland boss Mick McCarthy
"I'm surprised Carl Robinson was playing after his injury at Preston last week - although we knew when he came off that he was not concussed, just stiff and sore.
"So he's had a gentle week and he's ended it with a very good finish."
Leeds: Sullivan, Kelly, Butler, Carlisle, Crainey, Richardson,
Wright, Gregan, Pugh, Deane, Ormerod.
Subs: Carson, Ricketts,
Joachim, Spring, Duberry.
Sunderland: Poom, Wright, Stephen Caldwell, Breen, McCartney,
Whitehead, Whitley, Robinson, Carter, Elliott, Brown.
Myhre, Lawrence, Collins, Lynch, Bridges.
Referee: M Ryan (Lancashire)