Leandro Trossard (right) was the match-winner at Old Trafford
The Gunners delivered an unconvincing display against a severely depleted United side but did enough to secure the win that puts them one point ahead of Manchester City having played a game more.
Leandro Trossard struck after 20 minutes when lazy defending from struggling veteran Casemiro played Kai Havertz onside and his cross was turned in by the Belgian at the near post.
United showed plenty of endeavour but suffered from a glaring lack of quality and never seriously tested Arsenal keeper David Raya, as their own hopes of European football next season faded further.
Arsenal must now hope north London rivals Tottenham Hotspur do them a favour by getting a result at home to Manchester City on Tuesday.
The Gunners host Everton in their final game of the season next Sunday, while City are at home to West Ham.
-- Courtesy of BBC Sport