Antonio Conte's side opened up a provisional nine-point lead at the summit in the Boxing Day action.
Pedro struck either side of Eden Hazard's 50th English league goal at Stamford Bridge as Antonio Conte's side opened up a provisional nine-point lead at the summit in the Boxing Day action.
"To win 12 games in a row is not easy in this league," Chelsea manager Conte told the BBC.
"It's a fantastic run, but it's important to continue that now. In four days we have another tough game (against Stoke City) and we have to prepare very well. Because now, every team wants to beat you."
Olivier Giroud prevented Arsenal losing more ground, his 86th-minute header snatching a 1-0 win over West Bromwich Albion to lift Arsene Wenger's side above Manchester City into third place.
But with second-place Liverpool not in action until Tuesday, when Stoke visit Anfield, Manchester City can climb to second if they win at bottom club Hull City in the late game.
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.
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.
"In the end we had to be patient against a well-organised West Brom side. When you don't score early, you can't rush," said Wenger.
"We knew we had to win today after two disappointing defeats."
Manchester United sank 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 for his 17th goal of the season, before Henrikh Mkhitaryan sealed victory with a stunning 'scorpion kick' volley.
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.
"I didn't like the first-half performance. I like the result," said Mourinho.
"The players know the principles of how we play and they are comfortable, but we need to improve."
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.