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The Gunners sit 15 points behind runaway leaders Liverpool, now with just one game in hand, with their focus beginning to turn to holding off the chasing pack for a place in next season's UCL.
Bruno Fernandes' stunning free-kick put United ahead in first-half stoppage time. The Red Devils, though, could not hold on for just a sixth Premier League win in 16 games under Amorim as Rice swept home 16 minutes from time. A point leaves United down in 14th.
Arsenal boss Mikel Arteta was taking charge of his 200th Premier League match. The Spaniard's 118 wins in that time places him only behind a stellar cast of Pep Guardiola, Jose Mourinho, Jurgen Klopp and Alex Ferguson in the English top flight.
Arsenal had failed to score in either of their previous two league games to realistically wave goodbye to their hopes of a first title in 21 years.
