The win took Chelsea 10 points clear of Tottenham Hotspur who have three games remaining. Spurs will finish second if they beat United on Sunday afternoon at White Hart Lane.
Chelsea’s triumph comes at the end of Antonio Conte’s first season in charge at Stamford Bridge.
The former Italy and Juventus coach took over in July 2016 inheriting a squad at war following a disastrous title defence under former boss Jose Mourinho.
"This is a great achievement for the players," Conte told Sky Sports. "I thank them for their commitment and workrate. They showed me a great attitude to try to do something great this season.
"After this win we must be happy, we must be pleased. It wasn't easy for me to arrive in England and try different habits, a different language and players after a bad season."
Batshuayi, the understudy throughout the season to Spain international Diego Costa, had only been on the pitch for seven minutes when he scored the winning goal - his first in the league since August.
"It's good. It's the best day for Chelsea,” said Batshuayi, who arrived from Marseille last year in a 39.1 million euro transfer. "Everybody is happy. It's great to take the trophy."
Chelsea midfielder Cesc Fabregas said: "I thought it was going to be one of those days. We had so many chances in the first half and then we got a bit nervous.
"The beauty of football: a player who didn't play a lot scores the winning goal for the championship."
Chelsea have the chance to complete the league and cup double. They take on Arsenal on 27 May at Wembley in the FA Cup final.
"Every game I feel like I have played with my players," Conte added. "I show my passion and my will, my desire to stay with my players in every moment of the game. This is me.
"In the present, in the past, I stay with my players in positive and negative situations. We won this title together. We were not lucky, we did a great job. It is a great season and now we can win the FA Cup."