Rafa Benitez's men found themselves behind at the break thanks to Mohamed Salah's strike in first half stoppage time.
However, quick-fire goals from Fernando Torres, Victor Moses and David Luiz at the start of the second half put Chelsea in command and into their second successive European final.
Frank Lampard captained the side as he chased the goal that would equal Bobby Tambling's all time record and he had the first chance of the game on nine minutes, his scuffed volley rebounding off the post with Yann Sommer beaten.
Torres had an effort from distance smartly saved by the Basel 'keeper nine minutes later before Ramires shot straight at Sommer midway through the half following good work by Moses and Eden Hazard.
Basel appeared to be galvanized by Chelsea's profligacy and stunned Stamford Bridge by taking the lead with virtually the last kick of the half.
Valentin Stocker's neat through ball found Salah, who had seen an earlier effort saved, but made no mistake this time with a cool first-time finish beyond Petr Cech.
That meant for a nervy 15 minutes for the home crowd, who knew another goal for the visitors would send them through.
Whatever boss Benitez said at half-time worked wonders though as Chelsea stormed out of the blocks in the second half.
After 50 minutes Lampard's shot from the edge of the box was fumbled by Sommer, allowing Torres to slam home the rebound.
Just two minutes later Moses was alert to pounce onto Torres' blocked shot and convert into the corner from close range.
The goal of the night was reserved for Luiz seven minutes later, the Brazilian curling a wonderful fizzing effort beyond a motionless Sommer and into the top corner.
The three-goal blast knocked the stuffing out of Basel, allowing the Premier League side to see the game out and secure a meeting with Benfica at the Amsterdam Arena on 15th May.