Nuttall, who moved to Blackburn from Aberdeen during the summer and scored six goals in pre-season, netted Rovers' second in the 15th minute after Joe Rankin-Costello's opener.
Nuttall made it 3-0 in the 55th minute and completed his treble two minutes later.
Christian Herc replied for the visitors before Blackburn captain Lewis Hardcastle completed the rout with a superb long-range strike.
Joe Nuttall hits a hat-trick as Rovers U23s kick off the new season with a 5-1 win over Wolves at Ewood Park. 🔵⚪️➡️ https://t.co/rFD7sNDtRH— Blackburn Rovers (@Rovers) August 14, 2017
Blackburn are next in action when they face Reading at the Royals' training ground on Friday, while Wolves entertain Southampton at Telford next Monday night.
See: Blackburn report