Harry Kane’s penalty and Højbjerg’s late goal edged Tottenham past Everton with a 2-0 victory – to move four points clear of Chelsea in fourth spot.
Spurs were frustrated in front of goal for most of the match, with Antonio Conte’s side missing a host of chances as Everton goalkeeper was busy throughout.
Kane broke the Toffees’ resistance from the penalty spot after being tripped in the area by England team-mate Jordan Pickford, who had failed to hold on to Matt Doherty’s long-range effort.
Late in the game, Pierre-Emile Hojbjerg added a second goal with a curling effort that was slightly deflected into the goal by Alex Iwobi.
Despite early dominance by Spurs, the visitors had the two greatest chances of the first half and will be upset not to have converted both chances.
Following Demarai Gray’s unsuccessful attempt to connect with Conor Coady’s long pass over the top of the Tottenham defence, Hojbjerg’s errant touch allowed Amadou Onana to send a rocket over the crossbar.
Early in the second half, Kane fired a rasping volley straight at Pickford, but the Toffees goalkeeper was helpless to stop the 29-year-penalty, old’s which was his 14th goal against Everton in 15 Premier League games, or Hojbjerg’s late strike.
With the win, Conte’s squad moves up to a point behind north London rivals Arsenal and into a tie for second position with Manchester City, while Everton drops to 13th.