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Rangnick, who will make way at United for Erik ten Hag at the end of the season, has said he will also stay on in a consultancy role at the Premier League club.
Ronaldo's 62nd-minute strike was his 17th league goal this season with only Mohamed Salah of Liverpool having found the target more often.
United has been led by interim managers Michael Carrick and currently Ralf Rangnick since Ole Gunnar Solskjaer was fired in November.
An 82nd minute strike from Joao Moutinho earned Wolves their first win at Old Trafford since 1980 and moved Bruno Lage's side up to eighth place.
Rangnick steps in to replace Solskjaer, who was removed after United's 4-1 defeat by Watford this month.
Thomas Tuchel's Chelsea have 30 points from 13 games with City on 29 points and Liverpool, who beat Southampton 4-0 on Saturday, are a further point behind.
Former player Michael Carrick, a member of Solskjaer's coaching staff, will take charge of the United team for Tuesday's Champions League match away to Villarreal.
Manchester United suffered a fourth defeat in five Premier League games as they went down 4-1 at Watford to pile more pressure on manager Ole Gunnar Solskjaer.
It was ultimately a disappointing derby with City's superiority in all areas confirmed abundantly while Ole Gunnar Solskjaer's showed once again they simply lack enough quality to mount even a token title bid.
The 36-year-old Ronaldo has now scored five goals in four games for United in this Champions League campaign and has nine in 11 outings for the club this season.