Pedro struck either side of Eden Hazard's 50th English league goal at Stamford Bridge as Antonio Conte's side opened up a provisional seven-point lead at the summit following the Boxing Day action.
With Liverpool not in action until Tuesday, when they host Stoke, Pep Guardiola's Manchester City stole past them into second place by winning 3-0 at bottom club Hull City.
Olivier Giroud prevented Arsenal losing more ground, his 86th-minute header snatching a 1-0 win over West Bromwich Albion.
Zlatan Ibrahimovic scored one goal and set up two others as Manchester United closed to within three points of the Champions League places by beating Sunderland 3-1, while champions Leicester City lost again.
Chelsea's victory over Bournemouth left them one win short of Arsenal's 2002 record of 13 successive victories within the same top-flight season.
With Diego Costa and N'Golo Kante suspended, Conte paired Cesc Fabregas and Nemanja Matic in midfield, with Hazard starting up front, flanked by Willian and Pedro.
Pedro broke the deadlock in the 24th minute, curling a left-foot shot into the top corner from Fabregas's pass following a neatly worked corner.
Hazard made it 2-0 four minutes into the second half, rolling a penalty into the bottom-right corner after he had drawn a foul from Simon Francis, with Pedro adding a deflected shot in stoppage time.
Yaya to the rescue
Manchester City lost the recalled John Stones to an early injury and were made to sweat before three second-half goals secured victory at Hull.
Yaya scored a 72nd-minute penalty after Andrew Robertson fouled Raheem Sterling, with a Kelechi Iheanacho tap-in and a Curtis Davies own goal completing the win.
"There is always pressure for us because the top of the league is tough and the other teams at the top had won today," said Guardiola.
"Every game we play is like a final."
Meanwhile, beaten 2-1 by Everton and then City on their two previous outings, Arsenal narrowly avoided going three league games without winning for the first time since January 2012.
Alexis Sanchez's shot against the post looked to be the closest Arsenal would come until Giroud marked his return to the starting XI by looping a header over Ben Foster with four minutes to play.
Opening draw for Allardyce
Manchester United enjoyed a far less complicated afternoon, sinking Sunderland to record a fourth successive league win for the first time under manager Jose Mourinho.
Daley Blind opened the scoring in the 39th minute, striding onto Ibrahimovic's lay-off and steering a shot into the bottom-right corner.
Ibrahimovic got on the scoresheet nine minutes from time, slotting past Jordan Pickford to chalk up his 17th goal of the season, before Henrikh Mkhitaryan sealed victory with a clever back-heel.
United drew level on points with fifth-place Tottenham Hotspur, who visit Southampton on Wednesday.
Fabio Borini replied for the visitors, but it was a return to forget for Sunderland manager David Moyes, sacked by United in April 2004.
Sam Allardyce was denied victory in his first game as Crystal Palace manager after Troy Deeney's 100th Watford goal earned his side a 1-1 draw at Vicarage Road.
Ex-England manager Allardyce saw Yohan Cabaye put Palace ahead, but Christian Benteke had a penalty saved by Watford goalkeeper Heurelho Gomes before Deeney equalised from the spot in the 71st minute.
Champions Leicester's woes continued as they were condemned to a ninth defeat of the campaign by Everton, who won 2-0 at the King Power Stadium courtesy of Kevin Mirallas and Romelu Lukaku.
Leicester, who were without the suspended Jamie Vardy, have won just one of their last nine league games and sit three points above the relegation zone in 16th place.
West Ham United eased their relegation fears by winning 4-1 at second-bottom Swansea City through goals from Andre Ayew, Winston Reid, Michail Antonio and Andy Carroll.
Andre Gray's late effort gave Burnley a 1-0 win over Middlesbrough, the striker's shot squirming beneath visiting goalkeeper Victor Valdes.