United have been held to a 2-2 draw by Southampton at Old Trafford.
Southampton opened the scoring in the 12th minute, but United struck back twice before the break and appeared set for all three points until the visitors scored in stoppage time.
United remain fifth on goal difference behind Leicester, while Chelsea are another point ahead in third.
The top four qualify for Champions League football next season.
There are three games left.
Meanwhile Wycombe Wanderers have won promotion to the second-tier Championship for the first time after a 2-1 win over Oxford United in the League One playoff final at Wembley.
Wycombe, a non-league club until 1993, were promoted from League Two last season and secured victory thanks to a 79th minute penalty from Joe Jacobson.