Fabian Schar looked to have saved a draw for the hosts after Victor Moses' opener but the Brazilian ended their unbeaten run on home turf with the last kick of the match
Victor Moses' first-half header put the Blues in front but Fabian Schar looked to have salvaged a share of the spoils for the hosts from the penalty spot.
Fueled by the harsh decision to award a spot kick for Cesar Azpilicueta's foul on Valentin Stocker, however, Chelsea mounted a last stand and Luiz's 20-yard effort slipped away from goalkeeper Yann Sommer.
Basel lost at home for the first time in this year's Europa League.
Against a Basel team unchanged from their quarterfinal second leg against Tottenham, John Terry partnered Branislav Ivanovic at the back for the Blues as David Luiz moved into midfield, while Ramires and Moses started ahead of Juan Mata and Oscar.
Basel has proved to be a force both domestically and in Europe on home turf this season and sought to immediately take the initiative, but despite its dominance of the early possession Chelsea looked a potent force on the counterattack.
Cesar Azpilicueta was a persistent threat from right back and picked out a trademark Lampard run with a cross to the near post but Yann Sommer was equal to the midfielder's first-time effort.
From the resulting corner, however, determined decoy work by Ivanovic allowed Moses to sneak into space unnoticed to nod home Lampard's center.
Basel remained on the front foot but was largely restricted to shots from distance, with Fabian Schar forcing Petr Cech to tip his fiercely struck free kick over the crossbar.
Chelsea continued to find space on the right-hand side and soon after Fernando Torres' shot was blocked, Sommer did well to claw away Ramires' half-volley.
Eden Hazard spurned the visitors' best opportunity of the half when Moses set him through on goal but by that point Basel's control over proceedings had diminished.
Murat Yakin drew a brief response out of his team after the break and Stocker hit the post after a one-two with Marco Streller, but, once again, Chelsea effectively took the sting out of the game.
Chelsea, too, rattled the frame of the goal early in the second half when Hazard danced down the left and cut the ball back to Torres, who crashed a left-footed shot against the post.
Rafa Benitez was dealt one significant setback when Cole collected a booking for wasting time that rules him out of the second leg and his team was harshly punished by another refereeing decision before the final whistle.
With the Blues looking reasonably comfortable in defense, Stocker earned a spot kick under the challenge of Azpilicueta when it looked as if a cross from the right had evaded the Basel winger and Schar made no mistake.
Chelsea can take great credit, though, for the spirited response that drew. Both Torres and Terry were denied from point-blank range before Luiz's free kick escaped Sommer's clutches and nestled in the bottom corner.