Victor Moses put the Blues ahead early on as they looked comfortable for large spells in a composed display.
Late on Basel were handed a contentious penalty, which was duly dispatched by Fabian Schar to draw the Swiss champions level.
With the final kick of the match Chelsea snatched a winning goal when David Luiz sent a low free kick into the bottom corner.
Here, Sports Mole dissects just how the Blues were able to successfully build a 2-1 lead ahead of the second leg at Stamford Bridge next week.
On target: 3
On target: 9
Was the result fair?
On reflection Chelsea were in control for large parts of the match and probably deserved their two away goals, despite defending from deep throughout the second half. Basel will feel hard done by after a rousing late fightback, but in truth the home side were only able to create one clear-cut opportunity despite probing for most of the tie.
After a shocking start Murat Yakin's side grew in confidence and showed flashes of quality in wide areas. Valentin Stocker was hurried but forceful in the final third, while Fabien Frei produced a composed display in midfield. Defensively the home side struggled to defend crosses throughout, a fault ruthlessly exposed with the opening goal. Overall the Swiss champions should have cause for optimism that they are capable of scoring at Stamford Bridge to reignite the tie.
Rafael Benitez's side were disciplined, compact and broke with pace and purpose throughout the first half. Eden Hazard was a constant menace in a central role, while David Luiz and Frank Lampard provided effective protection for the back four. In the second half a stretched match saw Ashley Cole and Cesar Azpilicueta tested more frequently, with the equaliser on the cards despite the controversy surrounding the goal when it came. Chelsea led for more than 70 minutes and despite the game's dramatic conclusion the Blues used their experience to build an impressive advantage.
Sports Mole's man of the match
Victor Moses: The winger attacked with intent every time he got the ball and produced a composed, diligent performance throughout. He also provided support for the returning Cole throughout, taking the pressure off with menacing pacy bursts into the final third. On this evidence the Nigerian international is back to his best and pushing for a regular start in the Premier League.
Czech official Pavel Kralovec made two extremely poor decisions in the closing stages. After failing to show Luiz a red card for lunging in with his studs he awarded a penalty after Azpilicueta tangled with Stocker. The full-back cleanly cleared the ball but was somehow harshly penalised despite appearing to make a timely interception.
Kralovec is more than worthy of this accolade for an inexplicable penalty award, with Yann Sommer coming in at a close second place for failing to stop Luiz in stoppage time. The goalkeeper had a largely impressive game, but all his hard work was undermined as he was caught out at his near post after taking up a poor position behind his wall.
Basel: Yakin's side return to their title defence on Sunday against rivals Lucerne, before preparing for next week's return at Stamford Bridge.
Chelsea: The Blues must change their focus on the fight for a top-four finish this weekend, as Swansea City travel to West London.