London, England (SportsNetwork.com) - Manchester United took a big step toward securing a place in the top four on Saturday as Marouane Fellaini's goal in the 78th minute lifted the side to a 2-1 win over Crystal Palace at Selhurst Park.

United entered the match four points clear of Liverpool in the race for the final Champions League place, and Juan Mata put the visitors in front from the penalty spot in the 19th minute.

A free kick from Jason Puncheon in the 57th leveled the contest for Palace, and the hosts were pushing for a winner when Fellaini's header 12 minutes from time separated the sides.

The win moves United seven points clear of Liverpool, which needs at least a point at Chelsea on Sunday to keep the race alive.

Ashley Young played a role in both of United's goals on Saturday and it was his cross in the 19th minute that was handled by Palace defender Scott Dann inside his own penalty area, allowing Mata to slide his spot kick inside the left post and just beyond the reach of goalkeeper Julian Speroni.

Palace fought back and equalized in the 57th when Puncheon lined up a free kick and curled his shot toward goal from 20 yards. The ball took a slight deflection off the wall, but it was enough to throw off goalkeeper David De Gea and pull the home side level.

De Gea needed to be sharp to keep out shots from Glenn Murray and Wilfried Zaha as Palace searched for the go-ahead goal, but United hit on the break and snatched the winner 12 minutes from time.

Young once again did some good work on the wing and he served a ball toward the far post for Fellaini, who climbed above his defender to head home the winner from six yards.

At the other end of the table the relegation battle continued to take shape, and Burnley became the first team to be assured of heading down despite a 1-0 win over Hull City.

The reason the Clarets are headed to the Championship is that fellow relegation-strugglers Sunderland, Aston Villa and Leicester City each collected wins on Saturday.

Sunderland earned a 2-0 victory at Everton with goals from Danny Graham and Jermain Defoe, while Aston Villa used a first-half goal from Tom Cleverley to top West Ham, 1-0.

Riyad Mahrez scored twice in the first 20 minutes to help Leicester continue its fine form in a 2-0 win over Southampton, while Newcastle's 1-1 draw with West Bromwich leaves the Magpies two points clear of the bottom three.

The other contest on Saturday saw Stoke City hand Tottenham a 3-0 defeat at the Britannia Stadium with first-half goals from Charlie Adam and Steven Nzonzi before a late tally from Mame Biram Diouf.