The Blues prevented a third straight home defeat as goals from Jorginho, Tammy Abraham and Hudson-Odoi handed the west London side three points.
Callum Hudson-Odoi was full of joy after scoring his first Premier League goal in Chelsea's 3-0 win over Burnley on Saturday afternoon.
The Blues prevented a third straight home defeat as goals from Jorginho, Tammy Abraham and Hudson-Odoi handed the west London side three points.
The England winger, who returned from a ruptured Achilles earlier this season, made sure he finished off Cesar Azpilicueta's cross to wrap up the win and following the match at Stamford Bridge, the 19-year-old said: "I'm really delighted. Finally I've got it.
"I thought to myself that if no one touched it, it was goal. I'm delighted it went my way."
Chelsea are five points ahead of fifth-placed Manchester United, who sealed a 4-0 win over basement side Norwich City.
"We have to be more clinical, we always say that," Hudson-Odoi. "We got the chances we could have scored more.
"But at the same time we are putting them away. We were a bit more clinical and hopefully next game we'll try to get more."
He continued: "The boys put in a massive effort – the enthusiasm, the work rate. We all had it today.
"It was hard for us in the first 20 or 25 minutes to get on the ball and create stuff. In the second half here was more space and we started getting into pockets."