Ronald Koeman's first competitive game in charge of Everton ended all-square as Erik Lamela's header cancelled out Ross Barkley's opener to secure a point for Tottenham on the opening day of the Premier League season.
Despite an in-different pre-season that culminated in the sale of John Stones to Manchester City, Everton got the Koeman era off to the perfect start as Barkley's free-kick beat Hugo Lloris - the third consecutive time that the England midfielder has netted in the first game.
Everton, who won just six home games last term, continued to impress and Gerard Deulofeu should have put them further ahead when he got through on goal, only to fire a tame strike straight at Tottenham substitute goalkeeper Michel Vorm.
And the hosts were made to pay for their inefficiency in front of goal when Lamela restored parity with just over half an hour remaining with a well-timed diving header.
Tottenham dominated proceedings late on and, if not for two world-class saves by Maarten Stekelenburg that denied Vincent Janssen and Lamela respectively, would have sealed the three points.
Koeman, shorn of the injured Seamus Coleman and Romelu Lukaku, as well as new signing Ashley Williams, for Saturday's clash, had openly questioned the readiness of his squad in his pre-match press conference.
However, Everton showed no sign of any lingering fitness issues as they got off to a flying start when, after Kevin Mirallas was fouled by Tottenham debutant Victor Wanyama, Barkley's resulting free-kick evaded the Tottenham defence and floated into the right-hand corner of Lloris' goal.
Tottenham came on strong as they looked for a response but it was Everton who came closest to doubling their lead, Lloris called into action to deny Deulofeu before producing a superb finger-tip save to prevent Phil Jagielka heading in.
Bar the suspended Mousa Dembele, Tottenham were at full strength, but the visitors failed to test Stekelenburg until Christian Eriksen's effort was well-held by the Dutch goalkeeper.
Matters were made worse for Tottenham when Mauricio Pochettino was forced into a first-half change, with Lloris having to be replaced by Vorm after picking up a hamstring injury, and the former Swansea City man did brilliantly to prevent Deulofeu netting from close-range on the stroke of half-time.
Pochettino made a second change soon after the restart, with Eric Dier making way for new signing Janssen, the former AZ Alkmaar striker almost making an immediate impact as he teed up Dele Alli, but he could not keep his strike down.
However, Tottenham finally found their leveller just prior to the hour mark, Lamela stealing in ahead of Mason Holgate to head home Kyle Walker's cross.
Everton refused to let their heads drop, though, and Idrissa Gueye nearly capped a superb debut with a goal only for Wanyama to produce a wonderful last-ditch challenge.
Tottenham continued to build momentum as the game neared its conclusion, and would have taken the lead through Janssen if not for a terrific stop by Stekelenburg, with the Everton goalkeeper producing another stunning save to tip a Lamela strike onto the bar moments later.