Rafael Benitez’s team proved too strong for the Swiss minnows over the two matches and an aggregate victory of 5-2 reflected the difference in quality between the sides.
Chelsea’s place in the final, against Benfica in Amsterdam on May 15, leaves them on course for their second European trophy in two years.
The Europa League lacks the prestige of its richer, hallowed cousin, the Champions League, but victory in the Netherlands in 13 days would add considerable gloss to what has been a patchy, often poisonous, campaign.
Basel’s manager Murat Yakin suggested before the match that his team needed a "small miracle" to progress, and half-way through the second leg an upset was possible.
Mohamed Salah’s crisp finish for Basel in first-half added time levelled the scores on aggregate and put the tie in the balance.
But close-range finishes from Fernando Torres and Victor Moses, followed by an exceptional David Luiz strike, stretched Chelsea’s advantage to three goals and ended the hopes of the Swiss visitors.
Frank Lampard, who began the evening only one goal behind Bobby Tambling’s Chelsea record of 202, came close on several occasions to extending his haul, but, to the dismay of the home support, he was unable to do so.
Nevertheless, Lampard had the consolation of leading his team to the final in the absence of the benched John Terry, who made way for Gary Cahill and Branislav Ivanovic to be paired at the back, with David Luiz retained in midfield for the third consecutive game.
The resting of Juan Mata, who was named on Monday in the Professional Footballers Association Team of the Year, illustrated Chelsea’s confidence in extending their proud record of never having lost a home semi-final leg in European competition.
Rafael Benitez was shouting out instructions from the dug-out but, in the first half, it was the name of Jose Mourinho that was on the lips of the Chelsea supporters.
Chelsea threatened whenever they attacked but failed to convert the many chances that came their way in the opening period. Lampard hit the post with a half-volley, and Victor Moses, Eden Hazard and Ramires all squandered presentable opportunities to break the deadlock.
But it was not completely one-way traffic. As they demonstrated in their quarter-final win over Tottenham, Basel are dangerous on the counterattack.
Just as it appeared the first half would end goal-less, a fluent exchange of passes from Elneny and Streller put Mohamed Salah through on goal and he finished with aplomb.
Before the nerve strings could really begin to tug, Chelsea ended any hopes of an upset with three goals in quick succession after the break.
In the 50th minute, Torres scooped the ball into the net after Lampard’s shot from the edge of the box was parried by Yann Sommer in goal.
Moments later, Moses added Chelsea’s second following a powerful run into the box, a neat exchange with Torres and then a finish after collecting a fortuitous rebound.
At the hour mark, Luiz added some sheen to the win with an absolutely delightful left-footed curler from outside the penalty area. The finish, which arced beautifully around a defender and into the top corner, is a strong argument for keeping the Brazilian in midfield.