Tottenham, in fourth position, moved within three points of Liverpool despite conceding two second-half penalties in a 3-2 win at Wolverhampton.
Newcastle claimed its first league victory in 11 games by defeating Watford 1-0. Everton downed Brighton 3-1, and West Ham swept past Burnley 4-2.
SCHMEICHEL TEARS
The tears shed by Schmeichel summed up the mood at Cardiff as a huge banner, a Thai flag with "RIP Vichai" and the Leicester badge, was unfurled before the game.
Somehow, Schmeichel and his teammates managed to put their collective grief to one side to focus on football for 90 minutes and grind out a victory.
Demarai Gray scored with a low finish in the 55th and celebrated by removing his jersey to reveal an undershirt on which was written "For Khun Vichai." He was promptly booked by referee Lee Probert.
The Leicester fans sang Vichai's name for the rest of the afternoon and, at the final whistle, the visiting players came together to embrace.
"We were very close to the chairman," Leicester captain Wes Morgan said. "We know what his wishes were. He used to come down at home games, have a joke and a laugh, always say, 'Want win and three points.'
"It has not been an easy week, we had to try and hold our emotions in today and do the best we can."
LIVERPOOL HELD
Liverpool and fifth-place Arsenal had a first-half goal disallowed for offside in an entertaining clash at Emirates Stadium.
Milner eventually gave Liverpool the lead on the hour after goalkeeper Bernd Leno spilled a cross, but Alexandre Lacazette equalized with a curling shot in the 82nd minute after good work by the impressive Alex Iwobi.
"A point is a good result," Liverpool manager Juergen Klopp said. "When Arsenal chase the game they throw everyone on the pitch, which is really cool, and we were not as compact as I wanted."
UNITED RALLIES
Callum Wilson gave Bournemouth an early lead but United hit back against the run of play with a goal from Anthony Martial, his fifth in five games, in the 35th minute.
Substitute Marcus Rashford scored the winner two minutes into stoppage time at the end of the match after a surging run down the left and a pinpoint center from Paul Pogba.
TOTTENHAM HANGS ON
Goals from Erik Lamela, Lucas Moura and Harry Kane appeared to put Tottenham in an unassailable position at Wolverhampton.
The home team, though, caused an attack of the jitters for Tottenham after narrowing the deficit to 3-2 with penalties from Ruben Neves and Raul Jimenez, both awarded after fouls by 20-year-old Argentine center back Juan Foyth on his league debut.
OTHER MATCHES
Brazil forward Richarlison struck twice in Everton's win against Brighton, and Felipe Anderson's double guided West Ham to victory over Burnley. Ayoze Perez hit the only goal as Newcastle overcame Watford.
- AP