The Tottenham skipper must have feared for his place when Peter Crouch arrived at the club during the summer, but he has managed to regain his best form at just the right time and netted his first hat-trick in the league since December 2003.
The home side opened the scoring on 17 minutes. Jermain Defoe broke clear of Andre Bikey and was brought down inside the box. Referee Mike Dean had no hesitation in pointing to the penalty spot.
Keane made no mistake striking the spot-kick into the corner of the net.
Burnley thought they had grabbed an equaliser on 25 minutes when Steven Fletcher raced clear of the Tottenham defence and fired the ball past Carlo Cudicini, but his effort was ruled out for offside.
Jermaine Jenas has missed the start of the season through injury, but he wasted no time making an immediate impact on his return to the side when he scored the second on 32 minutes.
Niko Kranjcar saw his shot blocked by the Burnley defence. The rebound fell kindly to Jenas, who saw his fierce drive take a wicked deflection of Stephen Jordan and gave Jensen no chance as the ball flew into the bottom corner.
Burnley blew a golden chance to get themselves back into the game on 69 minutes.
Cudicini failed to hold onto a free-kick by Tyrone Mears and Robbie Blake reacted the quickest to the loose ball, but struck his effort against the post.
Burnley were made to pay when Keane added his second of the game on 73 minutes.
Aaron Lennon raced away down the right before cutting the ball back for the Tottenham skipper and he fired the ball into the roof of the net.
Keane grabbed his hat-trick on 77 minutes when he connected with a high ball over the top of the Burnley and beat the offside trap to fire a left-foot shot past Jensen
The Spurs striker made it a day to remember when he grabbed his fourth of the game on 87 minutes when he struck the ball through the legs of Jensen.