MANCHESTER, England — Jose Mourinho was in such good spirits after Manchester United beat Swansea that he invited rival manager Carlos Carvalhal into his post-match news conference.

“Come on, come on — give cakes to the guys,” Mourinho told his Portuguese compatriot after Saturday’s 2-0 win, referencing how Carvalhal handed out cake to reporters ahead of the game.

Romelu Lukaku scored his 100th English Premier League goal and Alexis Sanchez doubled the lead with his second goal for United as they responded to a win by Liverpool — United’s main rival for a second-place finish — earlier at Crystal Palace.

Lukaku is the 28th player to reach triple figures in Premier League goals. And, at 24 years and 322 days, he is the fifth quickest to get to that milestone after Michael Owen, Robbie Fowler, Wayne Rooney and Harry Kane.

“I’m really happy to achieve that in a league I’ve wanted to play in since I was six years old,” he said.

The Belgium striker ran onto Sanchez’s pass and scored with a deflected shot to put United ahead at Old Trafford in the fifth minute.

Sanchez, who had one of his best performances since joining from Arsenal in January, made it 2-0 in the 20th after being set up by Jesse Lingard.

David De Gea preserved United’s clean sheet with a couple of smart saves off substitute Tammy Abraham in the second half.

“We pressed so high and strong, and then recovered the ball,” Mourinho said. “We had lots of movement and passing. We arrived in many dangerous positions. We scored two; we should have scored at least one more.

“The second half was different. First of all, credit to Carlos because he improved the team at halftime. … I could feel the intensity went down. We let them have the ball, we didn’t press so high.”

United is two points ahead of Liverpool.