Goncalo Guedes netted the first goal of Pereira's reign, and Rodrigo Gomes and Matheus Cunha tripled the visitors' lead before half time, taking advantage of the Foxes' poor defensive display in the backline.
Wolves could have added to the scoreline in the second half, but the match was over as soon as the third goal went in, with Leicester devoid of any true attacking threat.
The result means that Wolves have leapfrogged Ipswich Town, rising to 18th place with 12 points, and they have just two fewer than Leicester, who are in 17th place.
SPORTS MOLE'S VERDICT
If any doubts remained, Wolves' win against Leicester is proof that the 'new manager bounce' is a real phenomenon, with Pereira overseeing his side's first win in their last five.
Though the visitors will spend Christmas day in the bottom three, it was absolutely vital that they picked up three points given their difficult schedule in the coming weeks.
Meanwhile, Leicester fans might not have warmed to previous boss Steve Cooper, but their defeat on Sunday highlights that many of the team's issues were not necessarily his fault alone.
The Foxes have looked alarmingly vulnerable defensively this season, having conceded 14 goals in their last five league fixtures, and Van Nistelrooy must address these issues if Leicester are to ensure their Premier League survival.
LEICESTER CITY VS. WOLVERHAMPTON WANDERERS HIGHLIGHTS
19th min: Leicester City 0-1 Wolverhampton Wanderers (Goncalo Guedes)
Conor Coady and Jannick Vestergaard watch the ball as Nelson Semedo plays a relatively harmless ball over the top of Leicester's defence, but the pair fail to take command of their box and allow Goncalo Guedes to swivel and strike the ball into the ground past goalkeeper Danny Ward from the right of the six-yard-box.
The first goal under Pereira!
36th min: Leicester City 0-2 Wolverhampton Wanderers (Rodrigo Gomes)
Wolves pick up the ball near the halfway line and play from the right of defence over the top of Leicester's backline, and Rodrigo Gomes sneaks past James Justin on the left of the box and pokes home past an onrushing Ward.
Calamity at the back!
44th min: Leicester City 0-3 Wolverhampton Wanderers (Matheus Cunha)
Wolves block Jamie Vardy's shot and race forward on the right through Semedo, who passes down the line to Guedes before the attacker works the ball to Matheus Cunha on the right side of the penalty area, and the Brazilian strikes fiercely from a tight angle, beating Ward.
That must be game over!
MAN OF THE MATCH - GONCALO GUEDES
While Leicester should have defended Goncalo Guedes's goal better, the attacker deserves praise for his patience, positioning and instincts in the box.
The Portuguese also managed to register an assist, taking control of Semedo's pass and delaying his layoff to Cunha until he had attracted enough pressure to give the goalscorer sufficient room to find the back of the net.
Guedes was also important from a defensive perspective considering he won three duels, made three recoveries and was only dispossessed once, preventing Leicester from getting a foothold in the match.
LEICESTER CITY VS. WOLVERHAMPTON WANDERERS MATCH STATS
Possession: Leicester City 54%-46% Wolverhampton Wanderers
Shots: Leicester City 9-8 Wolverhampton Wanderers
Shots on target: Leicester City 5-4 Wolverhampton Wanderers
Corners: Leicester City 6-1 Wolverhampton Wanderers
Fouls: Leicester City 15-16 Wolverhampton Wanderers
BEST STATS
WHAT NEXT?
After Christmas, Leicester face Liverpool on boxing day at Anfield, before they play struggling champions Manchester City at home on December 29.
As for Wolves, they are set to host Ruben Amorim's Manchester United in four days, and they take on Tottenham Hotspur next Sunday away from home.
Written by
Lewis Nolan