First-half goals from Amad and Dan Neil gave Tony Mowbray’s side a commanding two-goal lead at the interval, before the Clarets’ second-half comeback.
Nathan Tella’s header halved the deficit, before goals from substitute Manuel Benson and winger Anass Zaroury saw Vincent Kompany’s side take the lead.
Josh Brownhill then added a fourth with three minutes remaining.
Our Sunderland writer Phil Smith has dished out his player ratings from the Stadium of Light:
5. Dennis Cirkin - 4
Has made an excellent return from injury generally but struggled throughout this game and particularly against substitute Benson in the second half. 4 Photo: Frank Reid
6. Corry Evans - 6
Got around the pitch really well and helped cut out a number of Burnley’s moves. Like many, did little wrong but just contain the visitor’s individual quality in the end. 6 Photo: Stu Forster
7. Dan Neil - 6
Took his goal superbly and was part of a tenacious first-half performance. Caught on the ball for the fourth goal as Burnley ultimately overwhelmed the Black Cats. 6 Photo: Martin Swinney
8. Amad - 6
Took his goal superbly and battled well, but had very little impact on the second half as Burnley began to take control. 6 Photo: Frank Reid