Everton's Tomasz Radzinski spared the embarrassment of new goalkeeper Richard Wright after the £3.5m new boy looked to have gifted Spurs an unlikely win. Wright's fumble saw substitute Les Ferdinand give Spurs a lead they barely deserved after Everton dominated much of an entertaining encounter.
But Radzinski came to his, and Everton's, rescue to earn a point with a late equaliser.
David Moyes' Merseysiders looked on course for victory when Mark Pembridge gave them a deserved first half lead.
But Spurs turned the game upside down when Matthew Etherington and Ferdinand - helped by Wright - put Glenn Hoddle's men in front.
Radzinski then took charge with an excellent 81st minute leveller to ensure matters ended all square.
The day was memorable for Everton celebrating 100 years of top-flight football, and for the debut of talented teenager Wayne Rooney.
He lasted 66 minutes before he was substituted, but gave glimpses of the talent that has won rave reviews.
Rooney - not 17 until October - became the second youngest first-team player in Everton history behind Joe Royle when boss Moyes handed him his debut.
And he made an instant impact by troubling the Spurs defence and creating Pembridge's opener.
Spurs paraded summer signing Jamie Redknapp in midfield, while Everton had Wright and China international Li Tie on show.
The opening exchanges were predictably cautious, but Rooney demonstrated he was no respecter of reputations by clattering Teddy Sheringham at a corner.
But Everton moved into the ascendancy, and it was no surprise when they took the lead eight minutes before half-time as Pembridge crowned a sweeping move.
Thomas Gravesen sent Radzinski away down the right, and when he found Rooney the youngster was aware enough to find Pembridge, who finished in style.
Spurs suffered another blow in the dying seconds of the first half when defender Steve Carr, returning after a long injury absence, pulled a hamstring under persistent pressure from Rooney.
He was replaced by Ben Thatcher at the start of the second half.
Rooney was a constant thorn in Spurs' side, and he forced a fine diving save out of Kasey Keller after 53 minutes with a powerful 20-yard drive.
But this was to be the last bright moment for Everton in this period as Spurs turned the game on its head by scoring twice in 11 minutes to take the lead.
Spurs were level on 63 minutes as they worked the ball down the right before Redknapp laid the ball into space for youngster Etherington to lash high inside the near post and over Wright's head.
Everton boss Moyes then took off Rooney and opted for width in the shape of Swedish international Niclas Alexandersson.
But Hoddle's men were in front after 74 minutes when Ferdinand - a scourge of Everton throughout his career - beat Wright with a drive the goalkeeper should have saved.
But just as Spurs thought they had snatched victory, Radzinski pounced after good work by Kevin Campbell to equalise.
