David Luiz scored an injury-time free-kick to give Chelsea a precious lead from their Europa League semi-final first leg against Basel in Switzerland.
Chelsea led when Frank Lampard's corner hit the unsuspecting Victor Moses and flew into the corner after 11 minutes.
Fabian Schar equalised from the spot with three minutes left after Cesar Azpilicueta was harshly penalised for a challenge on Valentin Stocker.
But Luiz steered in a low free-kick to secure Chelsea a vital victory.
Basel will argue that Luiz, who played in midfield, was fortunate to be on the pitch after catching Philipp Degen on the shin with a challenge that referee Pavel Kralovec deemed only worthy of a yellow card 10 minutes earlier.
But equally the visitors would have had every right to feel hard done by if they had left Switzerland with a draw after Kralovec found fault with Azpilicueta.
Ashley Cole, who made his first start since sustaining a hamstring injury on 1 April, will miss next week's second leg at Stamford Bridge after receiving a caution for time wasting.
Chelsea, who have only failed to win a trophy in three seasons since Roman Abramovich took over in 2003, are attempting to become the first team to win the Champions League and then the Europa League in successive years.
The frustration for Rafael Benitez's side is that they had the chances to be returning to London with an even more comfortable advantage.
But given that Basel have beaten Bayern Munich, Manchester United and Zenit St Petersburg at St Jakob-Park over the past two seasons, this was an impressive evening's work for a team that had lost four of its previous five European away matches.
Basel won plenty of plaudits for their performances against Tottenham but they could never be accused of being negative and Chelsea ruthlessly exploited the home side's open defence on the way to taking the lead.
Hazard weighted a pass in behind Park Joo Ho for Azpilicueta to clip in a cross that saw Lampard's shot turned around the post by Yann Sommer.
But from the Lampard corner that followed, the ball dropped over Branislav Ivanovic and hit Moses in the face before bouncing into the corner of the net for his third goal in three Europa League matches.
As the hosts searched for a response, Schar's deflected free-kick was turned over the bar by Petr Cech, who also had to pull off a low save from Mohamed Salah.
But Chelsea had two fine opportunities to double their advantage before the interval, with Lampard finding Ramires and the Brazilian's shot being pushed away by Sommer before Hazard lifted over after a wild attempt at an overhead kick from Fernando Torres.
After the break, Stocker swapped passes with Marco Streller as he drifted in from the left and then saw his low drive glance away off the post.
At the other end Hazard made a fine run down the left and pulled back for Torres, whose stab at goal wrong-footed Sommer but hit the woodwork.
Chelsea were being forced ever deeper but were cruelly penalised when Azpilicueta appeared to steer a cross away from Stocker, only for referee Kralovec to award a penalty.
Schar made no mistake with the penalty but there was still time for Oscar to pass up a good late opportunity before Sommer pulled off a fine block from John Terry's header.
Yet a combination of a poor wall and Sommer's error allowed a Luiz free-kick to find the bottom corner in the fourth minute of added time.