Completing an unbeaten interim spell as Red Devils boss, the former Netherlands striker oversaw a comfortable success over the Foxes, where Bruno Fernandes opened the scoring with a slick finish into the far corner.
The Portugal international - making his 250th appearance for the Manchester giants - then appeared to bag a brace for himself later in the first half, but his header which took a significant deflection off Victor Kristiansen went down as an own goal for the Foxes defender.
Van Nistelrooy's side were not prepared to declare at two, though, as Fernandes then laid off Alejandro Garnacho to pick out the top corner of the net with an astounding strike from outside the area.
Despite managing to accrue four points from his two Premier League games as Man United manager, Van Nistelrooy cedes control of the reins to Ruben Amorim with the Red Devils sat 13th in the table.
Man United in worst league position before November international break
The 20-time English champions have now set an unwanted club record with their lowly placement, as they have never been in the bottom half of the Premier League table going into the November international break before the 2024-25 season.
While Man United have a 13-point deficit to make up to Liverpool in first place, they are still mathematically much closer to the European places than the relegation zone, currently occupied by Wolverhampton Wanderers, Southampton and Crystal Palace.
The Red Devils boast an eight-point lead over Palace in 18th place, while they are only four points below Chelsea and Arsenal in the top four after the London rivals' 1-1 draw on Sunday afternoon.
What the future holds for Van Nistelrooy is unclear, but what is for sure is that Amorim will officially be sworn in as Man United manager on Monday after his highly successful stint with Sporting Lisbon.
The Portuguese's final game in charge of the club ended in a 4-2 victory over Braga on Thursday, extending Sporting's 100% start to the Primeira Liga season, where they have won each of their first 11 games of the new term.
When is Amorim's first Man United match?
With the international break upon us once again, Amorim will have a couple of weeks to acclimatise to life in Manchester before he takes charge of his first game away to Ipswich Town on November 24.
The 39-year-old will then make his Old Trafford debut in the Europa League four days later, when Man United host Bodo/Glimt, and his first Premier League home game comes against Everton on December 1.
Amorim's remarkable work with Sporting has inevitably led to speculation that he could try to engineer January transfers for some of his standout stars, namely striker Viktor Gyokeres and teenage wing-back Geovany Quenda.
However, Amorim has affirmed that he will not be trying to lure any Sporting players to Old Trafford in January, and his top target is instead rumoured to be a former Manchester City man.