The only player who has achieved the feat earlier during Sir Alex’s reign is Wayne Rooney, who smashed three goals on his debut in a Champions League tie with Fenerbahce in 2004.
Recently-departed Michael Owen hit a treble in the Champions League win at Wolfsburg in 2009, in his 20th appearance but only eighth start. Seven matches into Andy Cole's United career, he hit five in the 9-0 trouncing of Ipswich in 1995.
Another of United's most prolific marksmen and van Persie's countryman, Ruud van Nistelrooy, needed 22 fixtures before scoring three against Southampton.
Watch all those goals, as well as hat-tricks from Dwight Yorke and Brian McClair, in our free video above.