Mauricio Pochettino kept faith with Harry Kane despite the striker's goal drought to start the season, and the England international had the first attempt of the game when he dragged wide from 25 yards.
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Only a superb Hugo Lloris save prevented Everton going in front against the run of play when the Frenchman denied Tom Cleverley his first Toffees goal by tipping the midfielder's effort over the bar after the former Manchester United man had robbed Kyle Walker.
Kane had a glorious opportunity midway through the half when he timed his run to perfection to get on the end of Ryan Mason's pass, but he hesitated when faced with Tim Howard and allowed the American to make the save.
Howard saved well again from Mason minutes later before stopping Bentaleb's shot as Spurs pushed for a breakthrough, before he had to turn Toby Alderweireld's header from a corner over the bar.
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Ross Barkley had an effort held by Lloris before the half ended in concerning fashion when Cleverley had to be stretchered off with his leg in a temporary cast following a challenge with Eric Dier, with Kevin Mirallas replacing the midfielder.
After the break, Spurs were dealt a blow when Dembele had to be stretchered off with an ankle injury. His replacement Dele Alli almost made an immediate impact, as he slipped Mason through on goal, who saw his low strike kept out by Howard.
Both teams pressed for a winner in the closing stages, but there were to be no further chances, as the match finished on level terms.