After a quiet opening 20 minutes at the Bayview Stadium, Wolves began to dictate the play, and were able to take the lead in the 31st minute as Bjorn Sigurdarson fired the ball in from close range after Jake Cassidy saw his effort blocked.
The Scottish side got back on level terms just before the break, with Andrew Jackson finding the back of the net from the penalty spot, having been brought down just inside the area moments earlier.
Leigh Griffiths restored the Molineux side's advantage at the start of the second half, scoring on his return to the club after two seasons on loan at Hibernian.
Griffiths was involved again in the 64th minute, delivering a corner which Tongo Doumbia was able to tap in from deep in the penalty area.
Wolves seemed to be in control heading into the final 15 minutes, but some strong defending by East Fife prevented them from finding a fourth goal.
However, the Scottish League Two side got back into the game in the 78th minute when Christian Nade picked up a stray pass and broke into the Wolves penalty area, smashing the ball past Aaron McCarey.
Wolves were able to keep the ball in the final minutes of the match to ensure that East Fife did not get back on level terms, ensuring a winning start to their new manager's reign.