Goals from Demba Ba and Andre Schurrle at Stamford Bridge were enough for the Blues to secure a place in the semi-finals of the competition
An early injury to Eden Hazard meant the introduction of Andre Schurrle and that substitution - no matter how coincidental - paid dividends for the Premier League side as the Germany international put the Blues in front.
Chelsea applied plenty of pressure in the second half, striking the woodwork twice before Ba's close-range finish with just three minutes to go, sending his side through to next round thanks to the away goals rule.
The Blues were available at around 2/1 (3.0) to qualify from the tie after losing the first leg 3-1 in the Parc des Princes and went off at 4/5 (1.80) to win the match. Jose Mourinho's men are now 13/2 (7.50) with Paddy Power to lift the trophy in Lisbon next month.
Real Madrid survived a scare, too, losing 2-0 to Borussia Dortmund in the second leg of their quarter-final clash. An early Angel Di Maria penalty miss was followed by two goals in 13 minutes from Marco Reus and set up a tense second half for Carlo Ancelotti's side.
Dortmund undoubtedly had their chances but a combination of Iker Casillas and the woodwork kept the Bundesliga side at bay and in the end Jurgen Klopp's men couldn't find the all-important third goal which would have forced extra-time.
Paddy Power make Real Madrid 23/10 (3.30) second favourites to win the Champions League with 17/10 (2.70) market principles Bayern Munich in action on Wednesday night against Manchester United, who are 5/1 (6.0) to qualify, despite drawing the first leg 1-1 at Old Trafford.
Despite an encouraging first-leg display from the Premier League side they remain rank outsiders against the Bundesliga champions. After pre-match 13/2 (7.50) quotes about them winning last week's first leg, some bookmakers have United as long as 11/1 (12.0) to secure victory in the Allianz Arena on Wednesday evening.
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Jim Knight is Betting Editor at Goal.com and has been tipping football games since he was old enough to place a bet. He is a Leicester City fan, writer and member of the We Are Going Up Podcast