Fred scored the only goal of the contest at Old Trafford, as the 20-time English champions secured an important three points under the leadership of their new head coach.
Rangnick has said that he was keen for his side to play with two strikers, with Bruno Fernandes pushing forward to join Ronaldo, and the German has hailed the 36-year-old for his contribution to the team in the one-goal success over Patrick Vieira's side.
"We always tried to be on the front foot. We were never not apart from maybe the last five minutes. At all other times we were trying to keep them away from our goal," Rangnick told BBC Sport.
"We wanted to play with two strikers, especially in the central position. By the way, Cristiano Ronaldo's work off the ball, chapeau."
Ronaldo has been in impressive form for Man United since returning to the club over the summer, scoring 12 times in 17 appearances in all competitions.