Chelsea boss Antonio Conte has said Diego Costa was not included in his squad for Saturday's game against Leicester City due to a back injury.
Alex Iwobi, Olivier Giroud and Alexis Sanchez impressed but Mesut Ozil was not quite back to his best as Arsenal thrashed Swansea.
Barton, 34, agreed to rejoin the Clarets earlier this month following an ill-fated spell with Rangers and came off the bench to score a free kick.
Watford were held to a 0-0 draw by Middlesbrough on an emotionally charged afternoon at Vicarage Road following the recent death of Graham Taylor.
Arsenal swept Swansea aside to keep their title challenge on track, with Olivier Giroud scoring once more and Alexis Sanchez also on target.
West Ham shrugged off Dimitri Payet's absence as an Andy Carroll wonder-strike helped secure a 3-0 win over Crystal Palace.