The Ivory Coast striker headed in a left-wing corner from Frank Lampard in the 61st minute to reach 151 goals for the Stamford Bridge club, one more than Peter Osgood and Roy Bentley.
Only Lampard, who also netted on Saturday to take his tally to 182, Kerry Dixon (193) and Bobby Tambling (202) have scored more goals for Chelsea.
Drogba, 33, who joined the London club from Olympique Marseille in 2004, limped off with an injury late in the game against Bolton and is rated doubtful for the midweek friendly international against Guinea in Abidjan.
Chelsea's victory over second-from-bottom Bolton eased the pressure on manager Andre Villas-Boas who recalled Lampard, Michael Essien and Ashley Cole to his team.
The Portuguese was widely criticised in midweek after he left the experienced trio out of his starting line-up as the side were beaten 3-1 by Napoli in their Champions League first knockout round first-leg tie in Italy.
NEW START
"The pressure has been on to get results recently," Villas-Boas said after his team claimed only their third win in 11 league games.
"Our run has not been impressive the last couple of games so the team wanted to go back to winning ways," he told the club website.
"This can mean a new start. It was important to win for the fans... and it was important they could go home smiling."
David Luiz opened the scoring for Villas-Boas's men with a curling right-foot effort in the 48th minute and Lampard sealed victory by tucking the ball in at the far post from a right-wing cross with 11 minutes left.
Lampard's goal was the 150th of his league career.
"It was a different formation today to the Napoli game where we had two defensive midfielders [Ramires and Raul Meireles] in front of the defence," Villas-Boas said.
"Today we were back to the normal 4-3-3 with fresh legs on the pitch. Lampard had his chance and played fantastically well.
"There are six players competing for three midfield positions. These decisions are taken for the benefit of the team," added Villas-Boas.
"Regarding Michael [Essien], his first game back after injury was against Sunderland. He then played against Manchester United and Everton and missed the Birmingham City and Napoli games.
"This was normal squad rotation."
