Swansea, which followed up a 1-0 win over Liverpool last week, climbed out of the relegation zone and into 17th place in the 20-team league.
A direct swap deal with no fee included, the former Borussia Dortmund player who spent two seasons under Mourinho will now sport the Gunner's crest, taking Sanchez's position.
The club announced the move on its website and blamed Everton's approach for Silva in November for "a significant deterioration in both focus and results."
City showed no sign of a lack of confidence following the 4-3 loss at Liverpool last Sunday as Aguero was on point to net in his 11th hat-trick for the club.
It was United's fourth successive victory while Burnley, who earned a point at Old Trafford on Boxing Day, slipped to their fourth straight loss of 2018.
Hazard was also involved in the second goal only three minutes later as some intricate link play ended with Brazil midfielder Willian producing a venomous right-footed shot that gave Brighton goalkeeper Mat Ryan no chance.
A week before it was both City and United who were in the race for Sanchez, but the league leaders backed out after the management felt that the wages demanded were too lofty.
Walcott, whose contract runs through to the end of June 2021, is the second high-profile signing by Everton in the January transfer window, after Turkey striker - Cenk Tosun.
Flanagan came through Liverpool's academy system and made his senior debut in 2011. He has played more than 50 times for the club but only once this season.
Manchester City didn't want to make Sanchez the highest-earning player at the club.
United moved three points clear of Chelsea and Liverpool in the race for qualification for the Champions League.
It was a first Premier League win over Arsenal for Bournemouth, and a first victory against a top-six side this season that lifts Eddie Howe's team into 13th place.
Manchester City threatened an amazing comeback after goals by substitute Bernardo Silva, in the 84th, and Ilkay Gundogan, in the first minute of stoppage time, but Liverpool held on in a nervy finale.
The England striker moved onto 98 goals, surpassing the previous mark of 97 set by Teddy Sheringham, thanks to two tap-ins at Wembley Stadium.
Despite Manchester City being favourites to sign the Chilean from Arsenal, Jose Mourinho has entered the race as he looks to sign both Sanchez and Ozil from the North London club.
The Everton outcast was supposed to join Chelsea in the summer transfer window but it was then manager Ronald Koeman who decided to keep the midfielder from being sold.
Son spared Tottenham from embarrassment in the 84th minute by cancelling out a similarly breath-taking strike from Pedro Obiang.
Wenger allegedly misbehaved after the match in the officials' changing room.
Ragnar Klavan headed home the winning goal at Turf Moor as Liverpool earned a hard-fought victory without three of its "Fab 4" attack, with Roberto Firmino demoted to the bench and both Philippe Coutinho and Mohamed Salah declared injured.
Failing to clinch their 19th straight victory, City could not equal the landmark set by Pep Guardiola's Bayern Munich in the 2013-14 season of the record winning streak in Europe's top five leagues.
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