The Londoners, like Benfica who face Fenerbahce in the other semi-final, were eliminated from the Champions League after the group stage, but both dropouts could yet meet in the final at the Amsterdam Arena on May 15.
Chelsea are well-placed after a 2-1 victory in Switzerland but Benfica trail their Turkish opponents 1-0.
Victory in the Europa League would not have been either club's target at the start of the season but it now offers redemption at the end of long and punishing road.
Chelsea, the outgoing European Champions, will be playing their 11th match in 33 days against the Swiss champions at Stamford Bridge.
Unless their tired limbs finally decide that enough is enough, they look set to book their place in the final and give interim coach Rafa Benitez the chance of a glorious exit.
Benitez has managed to rotate his squad and keep it fresh to challenge for both European honours and a place in the top four of the Premier League and a return to the Champions League.
A header from Victor Moses and a free kick from David Luiz deep in stoppage time gave Chelsea victory last week after Fabian Schaer's 87th-minute penalty for Basel.
Murat Yakin's men are attempting to become the first Swiss team to win a competitive match in England since 1995 - a run of 18 games without a win.
Basel have already enjoyed success against a London side though this season having knocked Tottenham Hotspur out of the competition on penalties in the quarter-finals after drawing 2-2 in London and 2-2 at home.
However, nothing less than an unlikely win will keep alive their chance of becoming the first Swiss team to reach a European final.
Thursday's match will be their 20th in Europe this season, a run which started in the second qualifying round of the Champions League away to Flora Tallinn in July.
"It's nice to win domestic leagues and cups but to qualify for the semi-finals of the Europa League is fantastic," said coach Yakin. "The players are aware that we can trouble every opponent we face. We're happy with what we've achieved so far and everything else is a bonus."
Benfica are still widely regarded as one of Europe's top clubs but it is 51 years since they last won a European trophy, lifting the second of their successive European Cups in 1962.
Their coach Jorge Jesus is likely to opt for the in-form Argentine duo of Enzo Perez and Nicolas Gaitan in midfield to help break down Fenerbahce after a surprising punt on rarely picked 33-year-old playmaker Pablo Aimar and teenager Andre Gomes did not pay off in the first leg.
Jesus blamed the 1-0 defeat in Istanbul on the juggling act he must perform to rest key players and keep the squad fit as they chase a memorable treble consisting of a Portuguese league and cup double and the Europa League.
Like Chelsea, Benfica are facing a burn-out scenario.
"Fatigue is our problem. We are fighting on all fronts," he said.
The rotation policy paid dividends on Monday in a rousing 2-1 league win at Maritimo that kept Benfica four points clear at the top with three matches to play meaning they could be crowned champions next week.
Although Dutch winger Ola John is suspended, the Eagles fancy their chances in front of their fans.
"Some important players were missing and we lacked our usual passing precision," Uruguay right back Maxi Pereira said about the first leg which Fenerbahce won with a second-half header from Egemen Korkmaz.
"Benfica have overturned worse results. We strongly believe we can reach the final," he added.
Fenerbahce, bidding to become the second Turkish side to win a European trophy after their arch-rivals Galatasaray lifted the UEFA Cup in 2000, will be without suspended midfielder Mehmet Topal, suspended striker Pierre Webo and ex-Chelsea midfielder Raul Meireles, who is injured.
Fenerbahce could have taken a bigger lead to Lisbon but for Cristian Baroni firing a first-half penalty against a post last week, and that miss could yet come back to haunt them at the Stadium of Light.