Chelsea will still be going through as it stands thanks to their two away goals, with the score tied at 2-2 on aggregate.
Basel started the match strongly but it was the hosts who nearly made the breakthrough on 10 minutes when Frank Lampard broke the offside trap before seeing his clipped effort hit the back post.
Chelsea were on the attack 10 minutes later, only for Fernando Torres's low shot to be turned away by visiting goalkeeper Yann Sommer.
Despite the home side taking control of proceedings midway through the half, Basel came close to scoring with 29 minutes played as Marco Streller guided his spectacular volley from a tight angle past the post.
However, they scored a vital away goal in first-half injury time when Mohamed Salah caught the Chelsea defence napping before slotting in calmly past Petr Cech.