Klinsmann, who netted in Tottenham's opening day victory Saturday, has now helped the team erase the six-point standings deficit imposed by the Football Association for financial irregularities.
"It was important to wipe out that punishment. Now we can start the championship," said Klinsmann, who transferred from AS Monaco in the offseason.
After Wednesday's matches, Tottenham and Newcastle United, which beat Coventry 4-0, now sit atop the league with six points apiece, though Tottenham effectively has zero because of the FA penalty. The points will be deducted at the end of the season.
Klinsmann's first goal came in the 21st minute when Darren Anderton's deep corner from the right was headed back from beyond the far post by Teddy Sheringham. Klinsmann failed to make contact, but was ready when Stuart Nethercott returned the ball, his overhead volley driving the ball past goalkeeper Neville Southall's right hand.
The second was put in 15 minutes later. David Kerslake crossed from the right, Nick Barmby flicked it on, and the German powered it home just inside the post.
Sheringham missed a penalty on the stroke of halftime, and Paul Rideout caught the Tottenham defense sleeping to score for Everton in the first minute of the second half.
Elsewhere, Newcastle United, without its captain Peter Beardsley who will be out for six weeks with a fractured cheekbone, was three up at halftime.
Robert Lee scored the first and third, while Beardsley's replacement Steve Watson hammered in an unstoppable right-footer for the second. England under-21 striker Andy Cole added the fourth in the 73rd minute.
England forward Matthew Le Tissier grabbed a brilliant 89th-minute equalizer in Southampton's 1-1 draw at Aston Villa, rifling the ball over goalkeeper Mark Bosnich from 30 meters.
Manchester City recovered from its 3-0 thrashing at Arsenal on Saturday by beating West Ham United by the same score at home.
England youth international striker Kevin Gallen scored the winner as Queen's Park Rangers won 3-2 at home to Sheffield Wednesday.
(AP, Reuters)
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