The Scotland international scored from close range after Michael Proctor had flicked on a right wing centre from Darren Williams, but it was to be the only time Brian Jensen was to be beaten.
The Burnley keeper was outstanding in keeping the Black Cats at bay with a series of spectacular saves, including a brilliant injury-time stop from substitute Marcus Stewart.
But it would have been an injustice if the home side had snatched a late victory from a game than both managers agreed could have finished 6-6.
Burnley hit the woodwork twice in the first half through Robbie Blake and Richard Chaplow, while goalkeeper Mart Poom made a superb save from David May's close range header.
Jensen's heroics started as early as the seventh minute when he pushed a powerful close-range header from Kyle around the post, but he saved his best for the second half, including an outstanding effort from Colin Healy.
He somehow pushed the Irish international's drive onto the bar and though Michael Proctor turned the loose ball into the net, he was ruled offside.
Burnley's equaliser in the 72nd minute was fully deserved, Ian Moore finishing off a well-worked move involving on-loan winger Luke Chadwick and the impressive Glen Little.
"It could have been 6-6,''enthused Burnley manager Stan Ternent. "It was a good point for us as we kept plugging away and we had our chances."