Chelsea moved back up to second five points behind United - but they beat Middlesbrough 1-0 only by the skin of their teeth.
Ricardo Carvalho gave the home side the lead, but in the second half Boro hit the woodwork on numerous occasions. Avram Grant's men managed to withstand the pressure in a desperate last few moments.
It took them above Arsenal, whose title hopes had teetered on the brink of extinction on Saturday. After trailing 2-0 with ten men, they came back to beat Bolton 3-2 to remain six points behind United after the 4-0 win over Aston Villa.
Elsewhere, Derby County were relegated following their 2-2 draw with Fulham.