The Thai businessman and four others died on 27 October, when the helicopter carrying them crashed outside the King Power Stadium shortly after taking off.
Most of Leicester's players, manager Claude Puel and senior staff are due to fly to Thailand for the funeral of Vichai, whose eight-year reign peaked in 2016 when the 5,000-1 outsiders became Premier League champions in astonishing style.
"Every single player wanted to get out there to be at the funeral", Leicester keeper Kasper Schmeichel said.
The only goal of game came in the 55th minute, when Demarai Gray notched from inside the area and celebrated with an outpouring of pent-up emotion.
"They were unified in their decision (to play the game Saturday), that it was important to them to pay respect to Vichai, by playing today and they've certainly made him proud in that sense".
"It's been a unusual week, surreal really, and I'm glad it's out of the way if I'm honest", manager Neil Warnock said.
A minute's silence was impeccably observed, with a wreath laid on the pitch and images of Vichai were shown on the scoreboards behind either goal amid the unfurling of a huge flag among the crowd in memory of the Thai billionaire. He used to come down at home games, have a joke and a laugh, always say, 'Want win and three points'.
"We all spoke about. wanting to play, it's what Vichai would've wanted and that's what we are going to do", striker Jamie Vardy told Sky Sports, adding that they would "honour his name" with their performance.
The Leicester players and staff also paid tribute to their former owner with the club's travelling fans after the final whistle.
"When we saw the flowers in front of the stadium - it is a family and the feeling that our chairman gave this club".
The Leicester manager spoke of his pride on Saturday (local time) and said his players had grown as people over the past week.
Manchester United fought back from one goal down to beat Bournemouth 2-1 at the Vitality Stadium as second-half substitute Marcus Rashford scored the victor in injury time.
Newcastle recorded their first league victory of the season, 1-0 over Watford, while Everton and West Ham United also won before Arsenal hosted Liverpool and Tottenham Hotspur travelled to Wolverhampton Wanderers in the later games.