West Ham's capitulation — after conceding two own-goals — keeps the team in fifth place, now two points behind Chelsea after playing its game in hand.
United, which is 14 points behind leader Manchester City in second, beat fifth-place West Ham 1-0. Leicester remains a point behind United after routing Sheffield United 5-0.
Victory over Arsenal in the north London derby kept Tottenham top of the Premier League in December.
Kjær capitalised on poor defending to head in a corner in the 92nd minute to give the Italian side a slight advantage ahead of the second leg next week.
Xhaka received a pass from goalkeeper Bernd Leno inside Arsenal’s penalty area and attempted a risky pass around Burnley striker Chris Wood to teammate David Luiz with his weaker right foot.
Arsenal started the day in 11th and returned to the top half with the win, while Leicester missed a chance to challenge Manchester United for second.
Manchester United drew 0-0 with Real Sociedad for a 4-0 aggregate win, and Milan progressed on away goals, 3-3 on aggregate, after drawing 1-1 at home with Red Star Belgrade.
Raheem Sterling took only 80 seconds to meet Riyad Mahrez's cross at Arsenal to clinch a 1-0 victory for Manchester City, who have won 18 games on the trot now.
Arsenal moved up a place into 10th with 34 points, snapping a two-game losing streak. Leeds, meanwhile, dropped down a spot to 11th with 32 points.
Emi Martinez, a goalkeeper sold by Arsenal in the last offseason, preserved Villa's win with several fine saves.
Leading 1-0 thanks to Nicolas Pépé’s 32nd-minute goal, Arsenal started its implosion when Luiz was given a straight red card for pulling back Willian José.
To make matters worse for Solskjaer's side, Manchester City on Saturday was able to do what United couldn't on Wednesday — beat bottom side Sheffield United.
Arsenal vs Manchester United Premier League Live Streaming: Find full details on when and where to watch ARS vs MUN Live Online on Hotstar and TV Telecast on Star Sports Select HD.
Odegaard has been at Madrid since 2015 — when he joined at the age of 16 — but failed to establish himself at the Spanish giant
Arsenal avenged a defeat to Southampton in the FA Cup at the weekend by beating the Saints 3-1 in the EPL.
The contract the 32-year-old Papastathopoulos had at Arsenal was canceled by mutual consent last week.
Ozil said goodbye to his Arsenal teammates a week ago and his move to Turkey has now been wrapped up.
In an otherwise close game, Gabriel's decision to try to block a shot from Kyle Walker-Peters proved decisive for Arsenal losing its hold on the cup.
Aubameyang, who hadn’t scored in the league since Dec. 16, broke the deadlock in the 50th minute before Bukaya Saka added a second with style in the 61st.
The former Germany midfielder, who is of Turkish descent, hasn’t played for Arsenal since March after falling out of favor with manager Mikel Arteta.
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