Alvaro Morata snatched a dramatic 91st minute winner moments after Bournemouth had equalised as Chelsea reached the EFL Cup semi-finals with a 2-1 win at Stamford Bridge on Wednesday.
Introduced in the 73rd minute, Spain strike Morata broke the visitors' hearts by combining with fellow substitute Eden Hazard to book his side's place in the final four.
The decisive goal came just 75 seconds after Dan Gosling had curled the Cherries level, appearing to reward Eddie Howe's men from a dogged second-half fightback.
But they were ultimately denied what would have been the club's first ever appearance in the next stage, with Chelsea instead still in contention for a second EFL Cup triumph in the space of four seasons.
Willian earlier capped a well-constructed move in the 13th minute to give his side a lead, which they held for almost the entire match.
And Bournemouth's disappointment will be compounded by the first-half loss of Jermain Defoe, who was forced off early following a heavy challenge from Ethan Ampadu.
Ampadu was brought in as one of eight changes for Chelsea and the teenager's first act was to go in late on Defoe, who was unable to continue beyond the 17th minute.
Chelsea were already ahead by the time of his substitution courtesy of a delightful team move.
Michy Batshuayi's pass enabled Kenedy to free Cesc Fabregas with a classy first-time back-heel and, from inside the area, the Spain midfielder unselfishly squared for Willian to tap home.
Defoe's replacement Jordon Ibe fired wide of the near post with a chance to issue a quick response, although the hosts quickly reasserted their dominance over possession and territory.
Batshuayi drew a close-range smother from Artur Boruc after being put through on an angle by Pedro, before Gary Cahill audaciously volleyed the half-clearance marginally over the bar.
Bournemouth survived to the break without further damage and returned with renewed impetus, winning a trio of corners in quick succession.
Lys Mousset drew another when his effort from Ibe's pass was deflected over the bar as Howe's men continued to grow in confidence.
Conte moved to alleviate the mounting pressure by introducing Hazard and Tiemoue Bakayoko in a double change, although the Cherries were inching closer to an equaliser.
Ibe first whistled a shot past the left post and Gosling went one better in the 90th minute, clinically curling beyond the outstretched Willy Caballero to spark wild celebrations among the away fans.
But their joy quickly turned to despair as, from the resultant kick-off, Chelsea stunningly restored their lead, Hazard skilfully setting Morata through for a cool one-on-one finish.
The striker's subsequent celebrations earned him a yellow card and a suspension, though, meaning he will miss Saturday's trip to Everton in the only dampener on the hosts' delight.
