Antonio Conte's side won plaudits for their display in the 1-1 Champions League draw against Barcelona in midweek, with the performance giving the Blues some much-needed momentum heading into back-to-back clashes against United and Manchester City.
Willian, who hit the post twice twice against Barcelona before scoring Chelsea's only goal of the game with a fine long-range effort in the second half, insisted that the Blues are capable of repeating their midweek performance at Old Trafford.
"It is totally different to play in the Premier League [compared] to the Champions League," the Brazilian was quoted as saying by ESPN.
"[But] I think we can stay at this level and we can go to Old Trafford on Sunday and play another great game. We have to play in a similar way.
"Against Manchester United, I think we can do a great job," Willian added. "Against Manchester City it will be like the game against Barcelona – they like to have the ball. We have to stay compact and use the same plan we used against Barcelona. We can win these games. We will go there to try to win."
Chelsea are in fourth place in the Premier League, 19 points behind leaders City. The Blues can move level on points with United with victory at Old Trafford.
Willian also revealed that he remains on good terms with Mourinho, whose second stint as Chelsea manager ended when he was sacked in December 2015.
"He is my friend," Willian said. "I had a great time with him, but I am at Chelsea and he is now at Manchester United."
Chelsea travel to the Nou Camp for the second leg of the Champions League round of 16 against Barcelona on 14 March.