The England international scored a first-half hat-trick, converting two penalties before adding a clinical finish in the 38th minute. Tolu Arokodare pulled one back after the break, but Palmer's early goals proved decisive.
The treble was Palmer's fourth Premier League hat-trick for Chelsea, moving him ahead of club legends Jimmy Floyd Hasselbaink, Didier Drogba and Frank Lampard. It also made him the first player in Premier League history to score three first-half hat-tricks, while his 44 league goals for the club moved him past John Terry among English scorers.
Rosenior, who has now won his first four league matches in charge, praised Palmer and his overall influence.
"I don't want him to change," Rosenior said. "We know what a world-class player he is. He's played a lot of football with little rest, but when he's at his best he's unstoppable. I'm delighted to be working with him."
Palmer, whose minutes have been managed following a groin injury, was substituted shortly after the hour mark. His celebration - covering his ears - appeared to respond to speculation about his future, though Rosenior insisted the forward remains happy at the club.
Since joining from Manchester City in 2023, Palmer has scored 44 goals in 84 appearances for Chelsea.
Palmer admitted he is still working towards peak fitness and credited Rosenior's impact.
"Not being 100 per cent fit isn't ideal, but when I'm fully fit I feel like I can go to another level," Palmer said.
Wolves boss Edwards added: "Not sure I like that lad very much. He's a special, special footballer."