In a city that was heaving with the World Watch and Jewellery Show, David Luiz timed his gem of a free-kick to perfection.
With the last kick of the match, the Brazilian took Chelsea closer to the Europa League final. Yet, it is debatable whether Luiz should have been on the pitch, having hurtled into a bad challenge on Philipp Degen.
After scoring early though Victor Moses, Chelsea had missed a host of chances and were punished when Fabian Schar converted a controversial penalty after Cesar Azpilicueta was adjudged to have fouled Valentin Stocker after 87 minutes.
The matches are coming thick and fast for Chelsea, so this was a huge away win. This tie was their 62nd game of a strange season for the European champions.
They host Swansea City on Sunday, before the Bridge return with Basel on Thursday when they will be without Ashley Cole, who triggered a ban after being cautioned for time-wasting midway through the second half.
Chelsea's run-in is hardly sprinkled with opportunities to draw breath, taking in Manchester United away, Spurs at home, Aston Villa away and Everton at home, not to mention the possibility of a European final in Amsterdam before the Everton game.
Chelsea had arrived at the neat and noisy St Jakob Park having lost their previous two away fixtures in the Europa League, but they started so positively. Eden Hazard was beating opponents with little bursts of pace, sudden changes of direction or applying that enhanced technique, let down only by some poor finishing.
Frank Lampard was lifting in some dangerous corners. Benitez, managing in his 137th European game, had paired Lampard and Luiz in central midfield. The Brazilian selflessly played the more disciplined defensive role, staying deep to keep an eye on Serey Die, while Lampard pushed on.
The Englishman was heavily involved in Moses' goal after 12 minutes. When Eden Hazard began the move, Lampard started his run from deep, venturing into the box in that familiar way of his. Hazard cleverly turned the ball right to Cesar Azpilicueta, whose quick cross to the near post was met by Lampard but Basel's defence had re-formed to block out the threat.
Lampard took the corner, hoisting in a ball that Branislav Ivanovic, rising more strongly than Park Joo-Ho and Fabian Schar, attacked, and the ball took a touch from Moses before eluding Mohamed Elneny on the line.
Ivanovic, thinking he had scored, jogged across to thank Lampard. Moses, meanwhile, celebrated acrobatically his third Europa League goal on the spin, having also found the mark home and away against Rubin Kazan.
Basel's fans behind the goal kept up their drum-driven support and the players responded, although Chelsea were largely in control of the first half. Touches of class occasionally spiced their play.
Basel, Spurs' shoot-out nemeses in the last round, emerged more powerful in the second half.
Chelsea's defence briefly lost all shape and concentration, giving Stocker the time to place a low shot against the post.
Chelsea should have made light of Basel's resurgence after 53 minutes. Hazard played the creator, cutting the ball back from the left to Torres, whose first-time shot cannoned against the post and out. The Torres of Liverpool would have swept that home unerringly.
Basel became more adventurous, Murat Yakin sending on attacking players like Marcelo Diaz and Jacques Zoua.
As they poured forward to their most vociferous supporters, Fabian Frei shot wide. Terry then reacted superbly to clear as Zoua threatened.
Chelsea tried to take the sting out of the game, slowing matters down. Cole took it too far, according to the Czech referee Pavel Kralovec.
Basel also lost an important player when Aleksandar Dragovic slid in for a tackle on Torres, winning the ball, and giving Basel a counter-attacking chance.
Benitez removed Hazard, sending on Juan Mata, and then withdrew Lampard for Oscar. Lampard walked off, shaking hands with Benitez, giving him a nod as well, as another opportunity passed to close on Bobby Tambling's Chelsea goalscoring record.
Ramires dropped back alongside Luiz.
With 11 minutes left, Mata lifted a free-kick to the far-post and it was met by a stretching Ivanovic, but he sent it just wide.
Chelsea's defence continued to stand firm. Ivanovic did brilliantly to hook the ball clear as Stocker was close to dribbling through.
Cole and Ivanovic twice cleared the danger before Luiz went in high on Degen, earning a yellow card and it could have been red.
Then came that late controversial penalty. Chelsea were furious, but they still had chances top regain the lead.
Oscar missed one and Terry went close before that wonderful free-kick from Luiz settled it. (© Daily Telegraph, London)