Arsenal were heading for a first defeat at their Emirates Stadium after Kevin Nolan fired Bolton into a 50th minute lead and were only saved by a 77th minute header from Kolo Toure.
Chelsea had no such trouble, with Ukraine striker Andriy Shevchenko giving the Premier League champions a ninth-minute lead. Goals from Ivory Coast striker Didier Drogba and Nigerian midfielder John Obi Mikel decided the tie before halftime.
Manchester City joined them in Monday's fifth-round draw after coming from behind to beat second division Southampton 3-1, while West Bromwich Albion are through after a 3-0 win over Wolverhampton Wanderers in a second-tier Midlands derby.
Arsenal will not relish their trip to the northwest and no love will be lost in the replay on February 14, St Valentine's Day.
Bolton, who hammered Arsenal 3-1 at the Reebok in the league two months ago, have been Arsenal's bogey team since a 2-2 draw in 2003 put paid to the title hopes of Arsene Wenger's side.
In the 10 games between them since then, Bolton have won four and drawn four, with all of their wins coming at home.
Nolan dug out a shot from the edge of the six-yard box after collecting a skewed Kevin Davies drive, following good work by former Arsenal striker Nicolas Anelka.
There was a dash of fortune with Toure's equaliser, the Ivory Coast defender stooping to meet a free kick with a downward header that looped back up and over keeper Jussi Jaaskelainen.
CHELSEA STRIKE
Arsenal manager Arsene Wenger told Sky Sports: "We lacked a bit of sharpness and focus in the first half and the pace of our game was too slow...but in the second half it was all us."
Bolton manager Sam Allardyce pinpointed a fine save by Arsenal keeper Manuel Almunia, denying Nolan a second goal just two minutes after he had found the net, as the turning point.
"That would have made it 2-0 and I don't think Arsenal would have come back from that," he said.
"We've got a great record against them, we've done fantastic here again today so we can hope we can keep it up."
It was a familiar story at Stamford Bridge, where Jose Mourinho's side had beaten fourth division Wycombe Wanderers 4-0 in midweek to reach the League Cup final.
Shevchenko, who scored twice against Wycombe, was on the score sheet again, though his close-range shot took a big deflection off Forest defender John Curtis, stranding keeper Paul Smith.
Drogba curled in an 18th-minute free kick for his 22nd goal of the season and Mikel poked in Chelsea's third from a metre out on the stroke of halftime following a goalmouth melee.
Forest made a better fist of the second half and their only scoring chance came in the 59th minute when striker Junior Agogo raked a low ball across the goal and the inrushing James Perch arrived just too late to steer it home.
Mourinho told the BBC: "In these kind of matches, like against Wycombe, we play serious. We don't let the opponent dream of a possibility (of an upset).
"We started the game very strongly and I think now we have a new enemy -- the pitch. We changed it two weeks ago and the pitch is not good enough. We have to solve it.
"It was very difficult to play good, fast football but the team played very well and we killed the game in the first half."