Last season's UEFA Champions League winners went in front when Branislav Ivanovic won a header which went in off Victor Moses, who claimed his third goal in as many Europa League games.
The visitors should have scored again prior to Fernando Torres striking the post before Cesar Azpilicueta was adjudged to have fouled Valentin Stocker and Fabian Schar converted an 87th-minute penalty. However, Chelsea responded and Luiz's late intervention earned the advantage ahead of next week's return at Stamford Bridge.
Basel seemed determined to enjoy their maiden European semi-final - in contrast, the tie is Chelsea's seventh in ten years - and the visitors were met with a raucous reception and energetic opponents. Chelsea had to be patient as Basel started well before Azpilicueta raced down the right and crossed to the near post, where Lampard's prod towards goal was turned away for a corner by Sommer.
Lampard's set-piece was met by Ivanovic, whose header deflected off Moses and bounced inside the far post. The Nigerian international forward, who scored in each leg against Rubin Kazan in the last round, knew little about the goal, yet cartwheeled away in delight.
Petr Cech tipped over a serving shot from Schar before the impressive Ivanovic had to be careful to avoid conceding a penalty as Stocker nipped in front of him. Basel were lively, with 6ft 6in captain Marco Streller the focal point up front. Streller appeared keen to celebrate his contract extension in style, but Ivanovic and Terry, supported by a retreating Luiz, dealt with the physical threat as Stocker buzzed around his strike partner.
Eden Hazard, playing centrally behind Torres, was doing his utmost to find openings in the Basel defence, but all too frequently Chelsea gave the ball away. Torres twice had half-chances before Lampard found Ramires and the Brazilian's dipping shot from the right was saved well by Sommer.
Benitez, who has a mind for statistics, will have been aware that 11 of Basel's 16 prior Europa League goals had come in the second half, and his Chelsea side were almost made to pay for their profligacy three minutes after the restart when Streller and Stocker combined and the latter hit the base of the post with Cech beaten.
Chelsea soon had another chance as Hazard rode the challenge of Philipp Degen and rolled the ball back for Torres to smash a left-footed shot off the inside of the post. Much of the second half was disjointed and punctuated by mistakes as Chelsea were forced to repel repeated Basel attacks.
Fabian Frei shot narrowly wide from the edge of the box and Cole received a yellow card for time wasting at a throw-in before Aleksandar Dragovic was booked for a sliding challenge on Torres, meaning the defender will now miss the second leg.
In a frantic final ten minutes Basel found themselves level when Azpilicueta was ruled to have hauled down Stocker in the area and Schar sent the ball down the middle of Cech's goal. Oscar shot narrowly wide and Terry's header was somehow stopped by Sommer before Luiz took his chance from 25 yards to belatedly give Chelsea the advantage in the tie.