The London football club are the defending champions of Europe after beating Bayern Munich in the final of the Champions League last year. Chelsea have a rare opportunity to become the first team to win the Champions League and the following year lift the Europa League title as well.
The Blues though had to rely on Thursday night on a last minute free-kick from Brazilian David Luiz to sneak past the home team, Basel, who equalised through a contentious penalty.
Victor Moses scored his third goal in as many Europa League matches to give Chelsea the lead in the 12th minute.
It seemed the Champions League holders would return home with a vital away goal and a win under their belt but Czech referee Pavel Kralovec had other ideas, awarding a bogus penalty to the home side.
Fabian Schar converted the 87th-minute spot kick to keep Basel's dream of qualifying for final alive.
However, Luiz's free-kick in the 94th minute beat Basel's wall of players and goalkeeper Yann Sommer, who was the man of the match.
Meanwhile, in Istanbul, Turkey's Fenerbahce defeated their Portuguese rivals Benfica 1-0 in the semifinal first leg.
The Turkish club, who missed a penalty in the first half, found the precious goal thanks to Egemen Korkmaz's header in the 71st minute, which gave them a narrow lead to take to Lisbon next week.