Dutch forward Robin Van Persie shot home from 15 metres in the 66th minute and Brazilian midfielder Edu scored in the dying moments to hand Arsenal a deserved victory.
With three games left, Arsenal moved on to 77 points, 11 behind newly crowned champions Chelsea but four clear of Manchester United, 4-0 winners at Charlton Athletic on Sunday.
West Brom stay bottom but one on 30 points, the same as Norwich City and one less than Crystal Palace and Southampton. All four clubs have two matches to play.
Chelsea clinched their first league title since 1955 with a 2-0 win at Bolton Wanderers on Saturday.
