Sean Dyche made two changes to the squad that won at Brighton, with James Tarkowski and Jay Rodriguez coming in for Nathan Collins and Maxwel Cornet.
In a tightly contested clash, captain Mee proved to be the match-winner when he steered his header from Josh Brownhill’s free-kick beyond Hugo Lloris to earn the three points.
Latest team news ahead of this weekend's game at Turf Moor
First-half
Burnley started strongly, and Dwight McNeil’s early strike from distance was charged down away for a corner.
Minutes later, Spurs captain Lloris had to grasp Aaron Lennon’s deflected cross, as the hosts pushed for an opener.
Lloris was then tested by Brownhill’s low effort from outside the box, after Connor Roberts’ long-throw fell to the midfielder.
Twenty minutes into the contest, Antonio Conte’s North Londoners created their first clear-cut opening, with Cristian Romero unable to hit the target having been played in by Dejan Kulusevski.
Midway through the half, Rodriguez shot from the edge of the box crept just beyond Lloris’ bottom right post following McNeil’s cross.
Spurs saw opportunities at goal go wide. Firstly, Emerson Royal’s rising shot didn’t test Nick Pope before a combination of Mee and Tarkowski denied Harry Kane in the six-yard box.
Play dropped to Brownhill on the edge of the box from Roberts’ neat pull-back, which Eric Dier got in the way of the shot.
Second-half
Spurs went narrowly close to taking the lead two minutes after the restart. Son Heung-Min’s right-sided free-kick was crossed into Kane, who beat Mee to the ball and flicked a header onto the top of Pope’s crossbar, which the Clarets cleared.
Burnley forced Lloris into action twice in three minutes. Wout Weghorst climbed above his marker at the back post to head Brownhill’s set-piece into the Frenchman’s grasp prior to keeping Mee’s downward header from McNeil’s free-kick.
Kane fired a warning sign into Pope’s side-netting from range, while our number one superbly thwarted Ben Davies from a matter of yards.
Mee was well-positioned to throw himself in the way of Kulusevski’s snapshot, as Erik Pieters pounced to clear to safety.
Son then won possession and charged towards Burnley’s backline to feed Kulusevski who clipped a low strike just wide of Pope’s bottom left-post.
The Clarets were in front on 72 minutes through Mee. The centre-back got the better of Cristian Romero at the back post to head Brownhill’s free-kick past Lloris and into the top right-corner to spark jubilant scenes around the ground.
Rodriguez went close to adding a second for the Clarets, but the forward diverted a shot over the crossbar after connecting with Mee’s ball.
Pope produced an excellent late diving stop to deny Steve Bergwijn’s strike which was bending in, before Lucas Moura struck over.
Burnley navigated the final few minutes to earn a second straight victory! Next up is a trip to Selhurst Park where Crystal Palace await on Saturday (3pm KO).
Burnley: Pope, Roberts, Mee ©, Tarkowski, Pieters, Cork, Brownhill, McNeil, Lennon, Rodriguez, Weghorst (Barnes 88)
Subs not used: Hennessey, Lowton, Collins, Bardsley, Long, Thomas, Stephens, Richardson, Barnes
Tottenham: Lloris ©, Romero, Dier, Davies, Emerson (Lucas Moura 65), Hojbjerg, Bentancur (Winks 45), Sessegnon (Bergwijn 79), Kulusevski, Son, Kane
Subs not used: Doherty, Reguilon, Sanchez, Rodon, Scarlett
Referee: Graham Scott
Goal: Mee, '72.