We take a lead into next week's semi-final second leg thanks to David Luiz finding the net with the last kick of the game in Switzerland.
Victor Moses had given the visitors the lead early in the game and it was an advantage we held into the final five minutes. Then Basel were awarded and scored a penalty, but the Blues deserve great credit for not settling for what would have been a healthy result at that stage. We had other chances for a late winner before the Brazilian scored our second.
The home team had looked capable of goals during the game, Chelsea even more so, and both sides hit woodwork early in the second half. It should be a cracking deciding 90 minutes back in London.
Basel named the same side that had begun their quarter-final second against Tottenham.
Urged on by a vocal support, the early pressure was from the home side, with Cech sent back-peddling as one over-hit cross landed on the roof of his net.
There were signs of nerves in the Swiss side however, playing in their first European semi-final, with misplaced passes in dangerous regions. Hazard showed signs of being able to give their defence problems, and David Luiz almost set something up for Torres after one particularly bad pass by the Basel.
On 11 minutes Chelsea sprang into life properly when a quick combination down the right by Hazard and Azpilicueta gave Lampard the chance to volley the full-back's cross at the near post. Yann Sommer in the Basel goal did well to push the ball wide for a corner. It was only a temporary reprieve.
Lampard sent the ball over into the mix where Ivanovic appeared to get the first touch. As it dropped down, Moses was able to divert it in from a yard or two out. It was his fifth European goal this season.
Now the Basel temperament was under examination and they responded to conceding that early away goal with some purpose. A free-kick save by Cech from Fabian Schar was made all the better by the fact it took a slight deflection off the Chelsea player charging it down. Terry rose high to head clear Basel's third corner of the game midway through the half.
It was down Basel's right that they looked the sharpest, and some nippy passing there inside our penalty area ended with Schar hitting the outside of the post from an acute with Cech in place and covering the net.
On the half-hour, Torres was released in a wide position. He cut back inside and shot but Basel had enough defenders back for an adequate block to be in place. Our number nine tired his luck from 25 yards out soon after but Sommer was looking sure-handed so far, having claimed a couple of corners well.
He was called upon to dive full-length to prevent Ramires making it 2-0 on 35 minutes. Moses had shown Basel a clean pair of heels down the left but his pull-back was slightly miss-directed. Lampard kept the attack alive with a pass to the Brazilian whose poke at goal needed a good save.
In the two minutes before the break the lead could, and probably should, have been doubled.
Torres was sent racing away just inside the Basel half and although he initially overran the ball, that lost his chaser and allowed him to pass wide. Torres then attempted to acrobatically convert the cross but didn't make proper contact. Hazard instead blazed over.
Moments later it was Hazard again with the chance, this time created by Moses, but with only the keeper to beat, he shot well wide.
Two minutes into the half Basel hit the post and this time Cech had been bypassed. Stocker, the Swiss side's wide-left player, made a darting run into the area and although initially held up by David Luiz, he was able to continue his run. His low shot had enough power to beat the Chelsea keeper, but thankfully lacked the direction - just!
Six minutes later it was our turn to rattle the woodwork. Hazard somehow stayed upright after being clattered on the run just outside the penalty area, and excelled in making the byline and picking out a team-mate, but from 10 yards out, Torres smashed a first-time strike against the post.
Basel could have made the Blues pay when Cech couldn't reach a high-flighted corner but their hefty centre-forward Marco Streller couldn't capitalise at the far post. Fabian Frei was not very far away with a long-range shot soon after. The Blues could not relax in this tie.
On 68 minutes Cole picked up the game's first booking for taking too long with a throw-in and it was a significant card. It rules the returning left-back out of the second leg. Basel centre-back Aleksandar Dragovic was also booked a minute later, much to the home fans' annoyance and he too will be suspended at the Bridge.
Basel were wasteful with quarter-of-an-hour to go. Schar played a ball behind Cole who couldn't catch Mohamed Salah but the winger took a strong touch and Cech was able to win the race for the ball.
Two more players were shown yellow soon after - neither facing a ban. They were substitute David Degen and David Luiz. With the ball back in play, Cole was sharp and well-positioned to keep Basel at bay when we looked vulnerable.
The Swiss side were turning the screw and kept the ball fizzing around our area. They were rewarded on 86 minutes when a nudge by Azpilicueta on Stocker was judged enough for a penalty, converted by Schar. It was 1-1.
The final minutes saw Chelsea attack strongly. Torres couldn't get a shot in from close range and then Oscar fired just wide. David Luiz swung a free-kick only a yard wide and then Terry had a header inside the six-yard box saved..
There was still time for one more free-kick and after the sickening feeling of Suarez's equaliser at Anfield just four days ago, it was a sweet moment when David Luiz's low strike found its way past the wall and past the previously impressive Sommer, who will not be pleased with his attempt to keep it out.
The St Jakob-Park stadium, which moments earlier had been rocking, fell very quiet apart from one corner containing the travelling support.
Tickets for the second leg in a week's time are currently on sale to season ticket holders and members, maximum three per person.
Chelsea (4-2-3-1): Cech; Azpilicueta, Ivanovic, Terry (c), Cole; Lampard (Oscar 79), David Luiz; Ramires, Hazard (Mata 70), Moses; Torres.
Unused subs Turnbull, Cahill, Bertrand, Mikel, Benayoun.
Scorers Moses 12, David Luiz 90+4
Booked Cole 68, David Luiz 83, Azpilicueta 87
Basel (4-3-3): Sommer; P Degen, Schär, Dragovic, Park Joo Ho; Elneny (Zoua 65), F Frei, Serey Die (Diaz 61); Salah (D Degen 78), Streller (c), Stocker
Unused subs: Vailati, Sauro, Cabral, Steinhofer.
Scorer Schar 87 pen.
Booked Dragovic 70, D Degen 80, Schar 89.
Referee Pavel Kralovec from Czech Republic.