Van Nistelrooy has replaced Steve Cooper at the King Power Stadium and saw Jamie Vardy open the scoring after just 98 seconds.
Bilal El Khannouss and Patson Daka added goals after the break to ensure the Dutchman started with three points in style.
His task is to keep the Foxes in the Premier League this season and after ending a five-game winless run they moved up to 15th, four points clear of the relegation zone.
"It has been very busy getting to know everyone ... but worth it," Van Nistelrooy said.
"I was focused on the game and what the game needed, the subs, the halftime talk, so focused on the moment, so I am going to get myself a little beer and reflect on the last three days.
"I am very happy, if you look at the result ... of course we have seen how dominant West Ham were at certain stages and what they created, that is a fact and something we have to look at."
Ruud van Nistelrooy looks on during Leicester's win over West Ham. (AP PHOTO)
Earlier on Tuesday night, Jean-Philippe Mateta fired Crystal Palace to a first Premier League away win of the season and left Ipswich Town still without a victory on home soil.
Mateta struck in the second half to secure a 1-0 success for the Eagles with the only real piece of quality in a nervy encounter between two struggling teams.
It was the French forward's sixth goal of the season, and his first away from Selhurst Park.
It is now two wins and three draws from the last six matches for Oliver Glasner's side, whose winter revival is gathering pace following a sticky start to the campaign.
"It's a big win. Now it's not time to sit back and relax but to keep going," Glasner said.
"In four days we face Manchester City ... There are still many things to improve but we are on the right path."
Jean-Philippe Mateta, that is INCREDIBLE 🤯— Optus Sport (@OptusSport) The Frenchman with his finest R9 impression to put Crystal Palace ahead.The step over. The dink. It's just beautiful.�Watch | https://t.co/UM954naBMC pic.twitter.com/8vmETQEug0December 3, 2024
Palace are up to 16th on 12 points, while Ipswich, who were missing Socceroos Massimo Luongo and Cameron Burgess, remain on nine and in 19th.
West Ham's hierarchy will have seen what impact a managerial change can have as the jury remains out on Lopetegui, with away fans making their feelings clear by chanting "You're getting sacked in the morning".
Niclas Fullkrug scored a consolation goal at the death but it counted for nothing and forthcoming games against Wolves, Bournemouth, Brighton & Hove Albion and Southampton could determine the Spaniard's future.
"I believe in these players and team, I am sure the position is going to be much better," Lopetegui said.
"They are only words but we have to work a lot to achieve this."
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