Leicester left Newcastle still rooted in the Premier League relegation zone with a 4-0 thrashing of the Magpies on Sunday, while West Ham's Champions League ambitions were dented by a 0-0 draw at Burnley.
Despite being hit by a coronavirus outbreak that left Brendan Rodgers without seven players, the Foxes gave Eddie Howe another reminder of the task he faces to keep Newcastle in the top flight as Youri Tielemans struck twice at the King Power.
Howe will be able to call on the resources of the Saudi sovereign wealth fund in the January transfer window and results elsewhere this weekend mean they remain just three points adrift of safety.
But Newcastle face Liverpool, Manchester City and Manchester United in their next three games and, on this form, will be lucky to escape that run without another severe hit to their goal difference.
Leicester had won just two of their previous nine games in all competitions and were dumped out of the Europa League by Napoli on Thursday.
However, they got the break they needed to edge in front before half-time when James Maddison engineered contact with Javier Manquillo to win a penalty.
With Jamie Vardy watching on from the bench, Tielemans took responsibility from the spot to open the scoring seven minutes before half-time.
Patson Daka's form has seen him earn his spot ahead of Vardy in recent weeks in the Premier League and Zambian had the easiest of tasks to roll in his seventh goal of the season from Harvey Barnes' unselfish pass to double Leicester's lead.
Tielemans rounded off a fine team move for his second of the afternoon before Maddison's fine finish compounded Newcastle's pain five minutes from time.
The victory lifts Leicester to eighth and back in the fight for a place in the top four while West Ham wasted the chance to extend their advantage over the chasing pack.
The Hammers have won just one of their last five league games as Nick Pope frustrated David Moyes' men with a string of saves at Turf Moor.
West Ham edged one point ahead of fifth-placed Manchester United, but Tottenham, who are not in action this weekend due to their own Covid outbreak, are just two points back with two games in hand.
A point also does little to aid Burnley's hopes of survival as they remain in 18th, but are now just two points adrift of safety.