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Sunderland started brightly and they were gifted an opener when Lukasz Fabianski played a goal-kick straight to Adam Johnson 20-yards from goal.
Johnson found Fabio Borini who's strike was only parried by Fabianski and Defoe made no mistake in slotting home the rebound to make it 1-0.
Sunderland looked like scoring with every attack, but they were undone by a controversial penalty decision after 21 minutes.
Andre Ayew burst into the area and went down, much to the bemusement of Wes Brown and the Sunderland defence, but the referee pointed to the spot and Gylfi Sigurdssson slotted home the spot-kick to make it 1-1.
The visitors were certainly unhappy with the award of the penalty, but it was the hosts turn to feel aggrieved minutes later when Kyle Naughton was shown a very controversial straight red card for a high foot.
The loss of a man didn’t seem to affect Swansea too much as they turned the game on its head five minutes before the break.
A long ball over the top was met by Ayew who turned Lee Cattermole inside out before firing home to make it 2-1 at the break.
However, Sunderland made the extra man count just four minutes into the second period when Patrick Van Aanholt cut inside and hit a rasping strike that flew into the top corner to make it 2-2.
And the Black Cats took full advantage after an hour when Defoe, who was a yard offside, raced in one on one and he again finished with aplomb to put his side 3-2 up.
The striker completed his hat-trick four minutes from time when Van Aanholt pulled the ball into his path and he slotted home to seal a vital 4-2 win for his side.
A late header from Robert Huth helped Leicester move level on points with Arsenal on top of the Premier League after as they beat Tottenham 1-0 at White Hart Lane.
Both sides created a host of chances, but it was Harry Kane who came closest to opening the scoring after an hour when he raced through one on one, but his effort was pushed onto the post by the brilliant Kasper Schmeichel.
And this saved proved vital seven minutes from time when from a corner, Robert Huth rose highest and produced a superb header to seal a 1-0 win for his side.
At the Etihad, Manchester City failed to close the gap at the top of the table as they were held to a goalless draw by Everton.
After a rather even opening 45 minutes, City were the better side after the break, but they were unable to find a way past an inspired Tim Howard.
A late strike from James McClean helped West Brom to a deserved point at Stamford Bridge as they drew 2-2 with Chelsea.
The Blues started brightly and they were rewarded after 20 minutes when Branislav Ivanovic raced down the right and whipped in a low cross that was turned home by Cesar Azpilicueta.
The Baggies, to their credit, refused to sit back and they continued to press forward at every opportunity and they leveled after 33 minutes when Craig Gardner smashed home a fine strike from 25 yards to send the sides in level at the break.
West Brom were the better side after the break, but they missed some good chances and they were punished with 17 minutes remaining when Willian’s cross was turned into his own net by Gareth McAuley under pressure from Kennedy.
The visitors again reacted well to going behind and they rescued a deserved point four minutes from time when James McClean swept home from the edge of the box.
Three second half goals helped Stoke to a hard fought 3-1 win over 10-man Norwich at the Britannia Stadium.
The hosts started brightly and their task was made a little easier after half an hour when Gary O’Neill received his marching orders for a needless scissor challenge on Ibrahim Afellay.
And the visitors were made pay early in the second half when Marko Arnautovic whipped in a sublime cross that was met by Jonathan Walters who steered his effort home at the far post.
But the visitors weren’t behind for long as they rallied and equalised when Johnny Howson produced a stunning volley to make it 1-1 after 55 minutes.
This parity didn’t last long, though, as Stoke retook the lead after 67 minutes when Joselu hit another fine strike from 25 yards.
And Mark Hughes wrapped up all three points 12 minutes from time when Afellay’s cross was headed into his own net by Ryan Bennett.
Goals in either half from Shane Long and Dusan Tadic sealed a much needed win for Southampton over Watford at St Mary's.
After a rather dull opening, the game burst into life when Matt Targett whipped in a sublime cross from the left that was met by a brilliant run from Shane Long and he headed home to make it 1-0.
Southampton dominated proceedings after this, but they had to wait until the 73rd minute to wrap up the three points when Dusan Tadic poked home.