Everton's winless run against Tottenham now stands at seven Premier League games after an evenly-matched 1-1 draw at Goodison Park on Sunday.
Mauricio Pochettino's side were the dominant force in the first half but were shocked when Aaron Lennon drilled home the opening goal with Everton's first effort of the game.
Roberto Martinez changed his side's shape with an hour gone in order to combat Tottenham's territorial dominance, though neither team looked ready to settle for a point as the contest became finely balanced.
The visitors were in complete control but it was Everton who snatched the lead on 21 minutes with their first shot of the game. Romelu Lukaku nodded down Tom Cleverley's long pass and Lennon, arriving from the right, looped a fine half-volley past Lloris and into the far corner.
Ben Davies thumped an effort off the crossbar from 20 yards but Spurs did manage a breakthrough just before half-time as Alli expertly controlled Toby Alderweireld's long ball before rifling a first-time volley past the helpless Howard.
Tottenham fully deserved their equaliser after dominating most of the first half and they continued to enjoy the majority of possession early in the second, though a half-chance for Kane following Alli's clever chest down was all they could muster in attack.
Alli stung the palms of Howard from 25 yards but Lloris was forced into a stunning save of his own as he tipped Besic's dipping effort over the crossbar, before Ramiro Funes Mori headed the resulting corner narrowly wide.
