An injury-time strike by David Luiz gave the Blues a second away goal as they look to progress to their second European final in two years following last season's Champions League triumph.
Frank Lampard's corner struck the head of Victor Moses and edged In at the far post, giving the visitors a dream start.
It appeared as though they would go home 1-0 winners until a controversial penalty was converted by Fabian Schar in the 87th minute.
Chelsea will now head back to Stamford Bridge with an air of confidence as they have not lost at home in European competition in 12 matches. On the other hand, Swiss champions Basel have not won away from home in the Europa League in their past eight outings.
2012/13 UEFA Europa League semi-final - first leg
St Jakob-Park, Basel - 36,000