Willian's first-half double moved Chelsea four points clear of fifth-placed Sheffield United in the race for the final Champions League qualifying spot.

Tottenham finished with 10 men after Son Heung Min was shown a red card for kicking out at Chelsea's Antonio Rudiger, who was then the victim of the alleged racist incident.

Willian opened the scoring at Tottenham Hotspur Stadium by curling in a shot in the 12th minute.

The Brazilian then added his second from the penalty spot after a video review ruled Spurs goalkeeper Paulo Gazzaniga had clattered Marcos Alonso.

Things turned a ugly in the 62nd minute when Son petulantly kicked up at Rudiger from the ground after a challenge between the two.

Rudiger then gestured to indicate he had been abused by the crowd and Blues keeper Kepa Arrizabalaga had an object thrown at him from the stands.

Referee Anthony Taylor came over to speak to both managers and three announcements were made stating racist behaviour was interfering with the game.

"It is made very clear to us all that if we have heard any racist incident to report it," Chelsea captain Cesar Azpilicueta said.

"Tony came to me and told me he was listening to racist songs towards him so I reported it to the referee.

"We are very concerned and aware of this behaviour. Altogether we need to make it stop."

Tottenham coach Jose Mourinho said he didn't see the incident but that the referee followed proper protocol.

"He came to (fourth official) Andre Marriner, he came to me and Frank Lampard and told us what was happening," Mourinho said.

"Every club is together in this situation and of course we are disappointed."

Tottenham later said in a statement that they are "conducting a thorough investigation" into the allegations of racism.

"Any form of racism is completely unacceptable and will not be tolerated in our stadium," the statement added.

"We take any such allegations extremely seriously and shall take the strongest possible action against any individual found to be behaving in such a way, including stadium bans."

The win for Lampard and his team meant he got one over his former Chelsea coach Mourinho, whose Spurs side sit seventh.

Earlier, bottom side Watford, under new manager Nigel Pearson, scored twice in four minutes to shock Manchester United 2-0 in the day's other match.

Ismaila Sarr and Troy Deeney struck early in the second half at Vicarage Road as the Hornets picked up just their second league win.

United keeper David De Gea gifted Watford's 50th-minute opener when he somehow let Sarr's scuffed shot to go through his hands, hit off his head and post and fall into the net.

The visitors' generosity continued a short time later when Aaron Wan-Bissaka fouled Sarr in the area and Deeney drilled home the penalty.

Watford remain bottom on goal difference behind Norwich but move within six points from safety, while United stay eighth.

Australian Associated Press