Anelka heads Chelsea four clear
The victory took Carlo Ancelotti's men on to 77 points with four matches remaining, four clear of Manchester United whose hopes of an unprecedented fourth successive title are fading fast.
Arsenal are six points behind Chelsea with one game in hand, against Tottenham Hotspur on Wednesday.
"It was a tough game, Bolton played their usual game, a lot of long balls, but we had 21 goal chances compared to their seven and deserved to win," Ancelotti told reporters.
"It was an important victory and three important points and takes us closer to the title. We were under a lot of pressure and I am delighted we've won."
Bolton manager Owen Coyle complained that his side were denied two penalties for handball, once by Didier Drogba and again by Chelsea skipper John Terry.
"They were not penalty claims, they were stonewall penalties," said Coyle.
"We did not deserve to lose that game tonight - it leaves us still looking for a couple of more wins to make sure we play Premier League football next season."
Anelka struck against one of his former clubs with a point-blank header two minutes before halftime when he broke free of static defending to meet Drogba's teasing cross at Stamford Bridge.
Bolton, who have now lost five of their last six league matches without scoring, remained just five points clear of the relegation zone and are not yet safe from the drop.
Ancelotti, whose side are chasing their first league and FA Cup double, went for an attacking line-up with Anelka and Drogba paired together for the first time in five matches and his ploy paid off with Anelka scoring for the first time since January.
Chelsea created the better chances on a balmy spring evening in west London, going close to taking the lead after 30 minutes when Bolton keeper Jussi Jaaskelainen parried a Drogba free-kick straight to Salomon Kalou who diverted the ball just wide.
Bolton, beaten 4-0 by Chelsea in the League and League Cup this season, appeared to be fired up by the words of Manchester United manager Alex Ferguson, who had suggested the league leaders may be facing an easy game.
But it was far from straightforward for Chelsea as Bolton fought for every ball and physically harassed the home side, with Russian defender Yuri Zhirkov bearing the brunt of their aggression.
He needed a bandage after clashing heads with Bolton striker Davies, but played on with blood seeping from the wound until he was told by the referee to get cleaned up.
Chelsea's Frank Lampard hit a post with a low drive after 79 minutes but a frenzied finish from both sides brought no further goals.