Sheffield United missed the chance to move up to fifth in the Premier League as they were held at home by struggling Brighton while Crystal Palace recorded a first win in 2020 with defeat of 10-man Newcastle.
Sheffield United took the lead through Enda Stevens but Neal Maupay equalised on the half-hour.
The result leaves Sheffield United in sixth place on 40 points, level with Tottenham.
Burnley won for the fourth time in five Premier League matches to lift themselves to eighth in the table.
Sean Dyche’s men scored all three goals in the second-half with Matej Vydra, Jay Rodriguez (penalty) and Dwight McNeil all on target.
Shane Long put Southampton ahead early against relegation-threatened Aston Villa and Stuart Armstrong doubled their lead deep into stoppage time.
Ralph Hasenhuttl’s men are 10 points clear of the drop zone. Crystal Palace, a point behind, eased their relegation worries with a 1-0 win over Newcastle who had Valentino Lazaro sent off late on.
In the early kick-off Olivier Giroud and Marcos Alonso were on target for Chelsea and Antonio Rudiger scored an own-goal as the Blues strengthened their hold on 4th place with a 2-1 win over Tottenham Hotspur at Stamford Bridge.
Pep Guardiola’s Manchester City take on third-placed Leicester at the King Power Stadium in the evening kick-off.
Manchester United, Wolves, Arsenal and Everton, who all harbour ambitions of qualifying for next season’s Champions League, are all in action on Sunday.
Runaway league leaders Liverpool host struggling West Ham on Monday.