The USA international netted his 50th Premier League goal for the Cottagers with a powerful 30-yard dead ball effort in the 12th minute as Martin Jol's side overtook Liverpool to move up to eighth position.
The Black Cats managed to hit back in fine style in the 34th minute when Phil Bardsley hammered home from range after being teed up by Ji Dong-won.
That sparked the home side back into action as they replied within a minute when Moussa Dembele attacked the top of the area before unleashing a well-struck attempt which took a deflection to send the ball into Simon Mignolet's top right corner.
Sunderland's Jack Colback came up with a headed goal-line clearance to deny Dempsey's left-footed volley in the 52nd minute before Fraizer Campbell had a brilliant chance to level for the visitors when he got on the end of Nicklas Bendtner's knock down only to put it wide of the target when all he had to do was beat Mark Schwarzer.
Craven Cottage, London - 25,683
Yellow cards:FUL - nil SUN - nil