Chelsea have assured themselves of a place in next season's Champions League after Arsenal were held to a 1-1 draw by Brighton at the Emirates.
Chelsea went ahead of Tottenham in the table but had to wait until the second half to open the scoring, as they bagged two goals in as many minutes to take control of the match.
Loftus-Cheek headed his ninth goal of the season from an Eden Hazard cross on 48 minutes, and the Belgian then set up Luiz for another headed finish two minutes later. Higuain then sealed the victory for Chelsea with a running pass from Pedro to chip the ball over the goalkeeper.
Arsenal took the lead in the first half through a penalty converted by Pierre-Emerick Aubameyang but they conceded a penalty for a foul on Solly March in the second half and could not break the Brighton defence to take a lead.
Arsenal however may still qualify for the Champions League by winning the Europa League.
United hopes for the top four ended after they were held to 1-1 draw by bottom side Huddersfield Town.
Manchester United's poor form continued this entire season and were unable to beat bottom side Huddersfield at the John Smith's Stadium.
Scott McTominay scored the first goal just eight minutes into the game when his shot slipped through goalkeeper into the box.Huddersfield took advantage by grabbing an equaliser from goal scored by Isaac Mbenza.The result makes for a disappointing end to the season for the United and will have to make drastic changes for the new EPL season.
Next season there is likely to be five teams from English Premier league representing Champions League if Arsenal wins the Europa League.
The Premier League title race will go down to the final day of the season after Divock Origi’s late winner for Liverpool at Newcastle on Saturday night.
City can ensure their destiny is in their own hands with victory at home to Leicester on Monday.
Manchester City is likely to become the second team after Manchester United to win back to back Premier League if they finish on the top of the table on final day of the season.
English Premier League standing for the top four on the last day of the season is likely to be Manchester City, Liverpool, Chelsea and Tottenham Hotspur.