Approaching the halfway point of the season Chelsea have 46 points to the 37 of Liverpool, who host Stoke City on Tuesday, and Arsenal, who needed a late Olivier Giroud goal to beat West Bromwich Albion 1-0.
Manchester City, who play at Hull City later on Monday, are on 36 points while Manchester United closed in on the leading pack, moving alongside Tottenham Hotspur on 33 after a 3-1 home win over Sunderland.
Pedro’s sumptuous chip put Chelsea ahead after 24 minutes before Hazard made it 2-0 with a penalty at the start of the second half.
Bournemouth, who won this fixture last season when Jose Mourinho was in charge at Stamford Bridge, gave it a go again but failed to break through and Pedro had the final say with a deflected shot in stoppage time.
Chelsea’s 12th victory took the winning run past the 11 they managed in 2009 and left them within two of the top-flight record set by Arsenal in 2002.
“To win 12 in a row is not easy in this league. It’s a fantastic run but it’s important to continue that now,” Conte said.
“In a few days we have another tough game (at home to Stoke on Saturday) and we have to prepare very well because now, every team wants to beat you.
“This is the first time we played without a real forward, we tried this in training and I think for us at the moment this situation is the best.”
Bournemouth manager Eddie Howe said: “They are an outstanding team and you can’t be too upbeat about getting beaten 3-0 but there were fine margins.
“Many elements of our game-plan worked but they have individuals of such quality that we couldn’t keep them quiet the whole of the game.”
It was a sentiment shared by West Brom boss Tony Pullis after his team delivered a terrific defensive display at Arsenal only to be undone by Giroud’s header four minutes from time.
“It is hard to take,” Pullis said. “Our supporters have seen us work so hard to stop one of the best teams in Europe so we are so disappointed not to see the game out.”
Manchester United were in command all day against Sunderland as former boss David Moyes had another disappointing day at Old Trafford but the game remained tense until the latter stages as the hosts missed a series of chances.
Daley Blind fired in the opener in the 39th minute but inspired goalkeeping by Jordan Pickford prevented further damage until Zlatan Ibrahimovic slotted the second.
Henrikh Mkhitaryan sealed United’s fifth straight win when he cleverly flicked in the third before Fabio Borini grabbed a last-minute consolation for Sunderland.
Leicester continue to struggle as they were beaten 2-0 at home by Everton despite dominating possession and the champions are now only two places and three points above the relegation zone.
“What a year. Everything was right for the first six months and now everything is wrong,” said Leicester manager Claudio Ranieri. “We have to fight.”
It was also an uncomfortable day for Bob Bradley as his Swansea side were crushed 4-1 at home by West Ham United to remain in the bottom two.
Burnley edged away from the danger zone with a 1-0 win over fellow-strugglers Middlesbrough and Sam Allardyce’s first match as Crystal Palace manager ended in a 1-1 draw at Watford.