The west London club were 3-1 down from the first encounter in San Paolo, but fought back bravely with support of the Stamford Bridge faithful.
Didier Drogba opened the scoring for the hosts in the first half, before captain John Terry doubled their lead early in the second half.
Gokhan Inler pulled one back for the visitors, but a Frank Lampard penalty forced the game into extra time. With penalties looming, Branislav Ivanovic proved to be an unlikely hero, popping up with the winning goal after 105 minutes.
Skipper Terry heralded the win as one of the best during his career at Stamford Bridge, and hit back at the team’s critics.
“This could top them all, for sure,” the England defender told ITV.
“The lads put in a great display, really solid, really resilient, with the firepower going forward.
“We proved we’re a team tonight. That desire, that togetherness. We showed what Chelsea are made of,” he stated proudly.
Frank Lampard was equally as impressed by the team’s performance, and applauded match-winner Ivanovic and the way he took his goal.
“We’re just happy to be in the hat. We’ll enjoy tonight and wait and see. If we play with that ability and desire, we can take on anybody.
“He (Ivanovic) finished it unbelievably, like a striker really. He deserved that, he was fantastic on the night and was a symbol of the determination we showed the way he played.
“It was important we showed a desire and spirit to keep ourselves in the competition. It’s been a difficult season but a performance like that can change things for us,” he stipulated.
The draw for the quarter-finals will be made on Friday in Nyon; the other teams in the mix are Barcelona, Real Madrid, Marseille, APOEL, Benfica, AC Milan and Bayern Munich.
By Gareth McKnight