Manchester United dropped to 13th in the Premier League standings and was just one place and two points ahead of Tottenham, which won 2-0 at Brentford to end a four-match losing run in the league and ease some pressure on manager Ange Postecoglou.
Vitaly Janelt scored an own-goal at a corner to put Tottenham ahead at half time and Pape Sarr added the second goal in the 87th.
“We needed a big effort again today, a physical effort. We put that in,” said Postecoglou, who rested defender Micky van de Ven after the defender returned from injury in the midweek win over Elfsborg in the Europa League.
“Outstanding effort by the players.”
The result was a huge boost for Tottenham ahead of arguably the team's biggest match of the season, the second leg of the English League Cup semi finals against Liverpool on Thursday.
Tottenham leads 1-0 from the first leg.
Ange Postecoglou, manager of Tottenham Hotspur, celebrates victory with Son Heung-Min. Getty
There have been calls for Aussie manager Postecoglou to be axed but the Spurs have so far indicated he won't be.
Meantime, after a recent uplift in their results, the pain returned for Manchester City and Manchester United in the Premier League.
City conceded a goal inside two minutes and was overwhelmed in the second half in a 5-1 loss at Arsenal, which trimmed the gap to leader Liverpool to six points.
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United lost again at home, 2-0 to Crystal Palace, and now has seven defeats in 13 league games at Old Trafford this season — something not seen since the 1890s.
The chances of City winning a fifth straight Premier League title are surely over — the champions are 15 points behind Liverpool with 14 matches remaining — and they must have felt humiliated by the end of the game at Emirates that again demonstrated the new-found hostility between Arsenal and City.