Redknapp's side suffer defeat on Merseyside
The home side were ahead after three minutes when Louis Saha fired in a superb strike from long-range to send Goodison into raptures.
However, this joy was to be short lived as Rafael van der Vaart equalised minutes later - heading in from close range after reacting to Peter Crouch’s flick on.
In the second half, Everton upped the ante and Coleman gave the home side a deserved three points after heading Saha’s parried shot past Gomes.
The three points move the Toffees up to 11th, while defeat for Spurs means they failed to take advantage of dropped points from Arsenal, Manchester City and Chelsea.
Everton came out of the blocks quickest and they took a deserved lead in the third minute. Leighton Baines found Saha in the middle of the field and the Frenchman struck a sublime 30 yard shot which flew past Gomes into the bottom right-hand corner.
Spurs responded straight away and Crouch should have done a lot better after heading Van Der Vaarts cross wide of the goal from six yards out.
They were not made to rue their missed chance as minutes later Hutton’s deep cross was headed across goal by Crouch where lurking was Van der Vaart to head home for his 10th goal of an impressive debut season in England.
Everton picked up their game after the equaliser and could have retaken the lead when Fellaini’s long-range shot was well saved by Gomes.
After good work down the right by Neville, Beckford should have got done better with his effort from inside the box which looped harmlessly into the hands of Gomes.
The Toffees were really in the ascendency and the Spurs were at full stretch to deny Beckford and Coleman after wonderful passing build-up by the home side.
Tottenham were reduced to playing on the counter due to the home side's dominance in possession but could have doubled their total for evening had Modric not shot over from 20 yards after the Everton defence parted.
Beckford, who has struggled since his arrival in the Premier League from League One, showed his inexperience at the top-level when he was unable to get his header on target after more good work from Neville down the right, who along with Coleman gave Benoit Assou-Ekotto a tough evening.
Spurs however continued to threaten as Dawson’s long ball forward was knocked down by Crouch into the path of Van Der Vaart, who hit a first time volley which sailed over Howard’s goal.
Seconds later, Bale won the ball off Saha and crossed for Crouch who was free in the area and slotted home - only for the goal to be called offside which replays showed to be the correct decision.
The visitors were ending the half the better side and were unlucky to see Van der Vaart’s 40-yard free kick fly just over the bar.
Lou Easy | Saha's long-range strike sent Everton towards victory
In the second half, Everton again started the better and should have been ahead when Saha released Coleman down the right but the youngster could only fire straight at Gomes with Beckford unmarked at the back post
Spurs continued to persevere with their long ball game and again Crouch and Van der Vaart combined with the latter unable to beat Howard with a stern volley from just outside the area, as the American turned the effort just past the post.
Coleman again threatened down the right for the Toffees and his cross found Saha in the area and his shot was deflected wide by Hutton when it seemed destined for the back of the net.
Everton finally got their goal after a quick break away when Beckford found Saha who drove at the Tottenham defence and after his shot was parried by Gomes, Coleman headed in after 75 minutes.
Tottenham tried to press to get back into the game but were unable to find a way through a resilient Everton side, who truly deserved the three points after an excellent all-round display.
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