Liam Lawrence scored the opener on 26 minutes when he headed in at the back post after Sean Thornton's corner.
Jeff Whitley almost grabbed a second on 77 minutes, but his curling shot was well-saved by Brian Jensen.
Substitute Ade Akinbiyi was dismissed for violent conduct two minutes into his debut before Marcus Stewart sealed the win with a close-range shot.
Sunderland boss Mick McCarthy:
"We're top and it's nice but more than that it was a good performance. Burnley is a difficult place to come and play.
"We played very well in the first half, they changed to 4-4-2 in the second half and made it harder.
"But it was a great victory and we played good football."
Burnley: Jensen, Duff (Akinbiyi 80), Cahill, Sinclair, Camara, Valois, Grant (Roche 45), Hyde, Branch, Whittingham, Moore. Subs Not Used: Coyne, Pilkington, Scott.
Sent Off: Akinbiyi (83).
Booked: Roche.
Sunderland: Myhre, Whitehead, Breen, Caldwell, McCartney, Lawrence, Whitley, Robinson, Thornton (Welsh 71), Bridges (Brown 85), Stewart. Subs Not Used: Neill Collins, Alnwick, Danny Collins.
Booked: Caldwell.
Goals: Lawrence 26, Stewart 89.
Att: 12,103
Ref: I Williamson (Berkshire).