A first-half goal by Nikica Jelavic was enough for Everton to condemn Spurs to a third consecutive league defeat, raising question marks about their top-four credentials just weeks after Harry Redknapp's side were trumpeted as title contenders.
Chelsea began the post-Andre Villas-Boas era in the league with striker Didier Drogba sealing a 1-0 home victory over 10-man Stoke City to put them level on points with fourth-placed Arsenal who host Newcastle United on Monday.
Both sides are now only four points behind Tottenham Hotspur who almost snatched a draw at Goodison Park when former Everton striker Louis Saha stabbed a late chance against the post.
Liverpool's slender hopes of a top-four finish diminished with a 1-0 defeat at Sunderland for whom Nicklas Bendtner scored the winner while Aston Villa earned a 1-0 victory over Fulham that moved them away from the danger zone.
Tottenham, after consecutive defeats at Arsenal and at home to Manchester United in which they conceded eight goals, had their hopes of getting back on track undermined by a lethargic first-half performance at Everton.
The hosts took the lead after 22 minutes when Jelavic steered in Leon Osman's cut back to score his first goal for the club following his move from Rangers and although Spurs dominated after the break they could not find an equaliser.
It is the first time they have lost three league games in a row since Redknapp took over in October 2008.
"We battered them second half but couldn't get a break in front of goal," he told ESPN. "It was one-way traffic second half ad they couldn't get out of their half."
Drogba's 100th Premier League goal made it a satisfying week for Chelsea caretaker manager Roberto Di Matteo, upgraded after Villas-Boas last week paid for a poor run of form with his job after just eight month at the helm.
Di Matteo relied on the old guard of Drogba, Frank Lampard, Ashley Cole and John Terry, back after injury, to see off Stoke who played three quarters of the match a man light after Ricardo Fuller was red-carded for a stamp on Branislav Ivanovic.
"Today was a step in the right direction, we got three points, and sometimes in a season you have to win like this to get the three points, it is not always going to be easy," Di Matteo, whose side had an average age of 28-and-a-half, told Sky Sports.
"Sometimes you have to win a little bit scrappy."
Two relegation battles produced precious wins for Bolton Wanderers against Queens Park Rangers and Blackburn Rovers at Wolverhampton Wanderers and more ammunition for those seeking the introduction of goal-line technology.
Bolton's 2-1 victory, sealed in the 86th minute by Ivan Klasnic, was overshadowed by a 'ghost goal' for QPR
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