The reigning Champions League winners took a 2-1 lead into the return bout after scoring a late goal at St Jakob-Park last week and despite conceding the first goal tonight, ended up with a 5-2 aggregate triumph.
Mohamed Salah, who is attracting the interest of some English clubs, levelled the tie for the Swiss champs on the stroke of half-time when he received a neat through ball from Valentin Stocker to expertly finish past Petr Cech with a first-time effort.
However, it took the Blues just five minutes of the second half to get their noses in front with Fernando Torres providing the killer blow with a well-taken sliding finish after Basel keeper Yann Sommer parried Frank Lampard's well-struck attempt.
Two minutes later and it was 2-1 on the night to Chelsea when Victor Moses, who scored in the first leg, took two goes to fire the ball past Sommer after his first effort was blocked. That preceded a stunning goal from David Luiz just prior to the hour-mark following on from his fine free-kick last Thursday.
Lampard teed the ball up for the Brazilian to hit a perfect left-footer from range, curling just inside the left upright, giving Sommer absolutely no chance whatsoever.
2012/13 UEFA Europa League semi-final - second leg
Stamford Bridge, London - 39,403