Manchester City moved back one point clear of Liverpool despite not being at their fluent best.
Manchester City have a game in hand, at home to Leicester City on Monday, but Liverpool refuse to give up in their pursuit of a first Premier League title for 29 years.
Manchester City moved back ahead of Liverpool to the top of the Premier League with a 1-0 win at Burnley
Newcastle moved 10 points clear of the relegation zone thanks to Ayoze Perez's first-half header at the King Power Stadium.
Danny Drinkwater was arrested early Monday morning after what police termed a "one-vehicle incident" on his way back to his home near Manchester following a charity event.
Brendan Rodgers was given a tough welcome back to the Premier League when substitute Andre Gray pounced on Troy Deeney's fine through ball.
Brendan Rodgers was confirmed Leicester City manager just before kick-off at the King Power after dramatically leaving Celtic.
Leicester City's dip in form followed a promising period over Christmas when they beat both Chelsea and Manchester City.
Manchester City demolished Chelsea 6-0 to go top while Tottenham Hotspur cemented their third place with a 3-1 win over Leicester City.
Manchester United's 1-0 win helped them move above Arsenal into fifth while Manchester City beat Arsenal to leapfrog Tottenham into 2nd.
Jeffrey Schlupp, Andros Townsend and Luka Milivojevic were the goal scorers for Crystal Palace.
Pep Guardiola's side took the lead when Kevin De Bruyne marked his return from injury with a fine finish in the first half at the King Power Stadium.
Vichai Srivaddhanaprabha was among five people killed when his helicopter crashed outside the King Power Stadium on October 27.
The charismatic Thai had become a beloved figure in the club and the city.
Kasper Schmeichel said Vichai Srivaddhanaprabha transcended the traditional image of a Premier League club owner.
Vichai Srivaddhanaprabha died last week, along with four others, when his helicopter crashed after taking off from Leicester's pitch following a match.
Leicester City's Midfielder Demarai Gray was booked by the referee in the 55th minute of Premier League game against Cardiff City
Leicester's players huddled together in celebration at full-time, with many of them due to fly to Thailand to join Vichai's funeral.