Leicester travelled to the London Stadium with the second-worst defensive record in the top-flight, and that glaring weakness was exposed in the 21st minute when Tomáš Souček, on his birthday, opened the scoring despite the best efforts of Mads Hermansen.
The Foxes goalkeeper made a smart stop to thwart Mohammed Kudus after he had been played onside by Jannik Vestergaard, but no Leicester defender reacted quick enough to stop Souček from tapping home from the rebound.
The Hammers maintained their slender lead with minimum fuss against a passive Leicester side, even doubling their advantage through a Vestergaard own goal in the closing stages of the first period.
A near-post corner kindly dropped for Jarrod Bowen, who squeezed it home from a narrow angle with the aid of a crucial deflection off the Danish defender, leaving Van Nistelrooy with an unenviable half-time team talk.
Surprisingly, the Leicester boss opted against making changes at the break, leaving it until the 61st minute before he turned to Harry Winks and Stephy Mavididi in the hope they could spark an unlikely fightback.
The Foxes certainly showed greater intent following those alterations, with Vestergaard producing a goalbound header from a corner in a rare moment of promise for the travelling support.
However, Alphonse Areola comfortably gathered the effort in a simple evening for the West Ham goalkeeper, who celebrated back-to-back clean sheets as the hosts saw out the contest to seal consecutive league victories for the first time since March.
Graham Potter’s charges move up to 15th, while the Foxes remain five points adrift of safety.