Liam Lawrence headed Sunderland in front with his sixth goal of the season after a shot from striker Marcus Stewart was deflected off Burnley's Peter Whittingham and Micah Hyde.
Burnley boss Steve Cotterill introduced £600,000 signing Ade Akinbiyi as the Clarets pressed for an equaliser, but the striker's debut was to last for only two minutes 38 seconds before he was shown the red card for a violent attack on Sunderland defender George McCartney.
Stewart rubbed salt into the wounds with his 13th league goal of the season in the 89th minute after Burnley central defender Gary Cahill appeared to be blatantly fouled by Jeff Whitley.