A controversial late penalty from Fabian Schar looked set to give Basel a draw, but Luiz's dramatic stoppage-time contribution put Chelsea in control after Victor Moses had opened the scoring in the first half.
Chelsea took the lead on 12 minutes following a fine move when Cesar Azpilicueta's cross from the right was flicked towards goal by Frank Lampard and pushed behind by Yann Sommer.
From the resulting corner, Lampard's delivery was missed by Branislav Ivanovic, but struck the head of Moses and bounced inside the far post.
Petr Cech tipped Schar's thunderbolt over the bar on 17 minutes before Fernando Torres shot straight at Sommer just past the half-hour mark.
The Blues could have scored twice more before half-time when Ramires was found in space in the box 10 minutes before the break, but the Brazilian's flicked volley was kept out smartly by Sommer.
A minute before the interval, Torres and Moses combined superbly to play Eden Hazard down the middle, but the Belgian's touch let him down and he dragged his shot wide.
Within three minutes of the restart, Basel could have been level when Valentin Stocker played a neat one-two on the edge of the box before scuffing his shot against the post.
Chelsea were denied by the woodwork on 54 minutes when Torres was picked out unmarked following an excellent run by Hazard, but the Spaniard's left-footed shot cracked against the upright.
The fit-again Ashley Cole was booked for time-wasting on 69 minutes and will miss the second leg as a result, while Basel defender Aleksandar Dragovic will also sit out next week's game at Stamford Bridge after picking up a yellow card for a lunging challenge on Torres.
Basel upped the pressure inside the final 10 minutes and were rewarded with three minutes left when Schar converted from the penalty spot after Azpilicueta was harshly adjudged to have fouled Stocker.
Chelsea were presented with an immediate chance to regain the lead, but Torres was unable to get a clean shot away and then substitute Oscar scooped the ball over the bar.
In stoppage-time, a brilliant reaction save from Sommer denied captain John Terry from close range, but the Basel keeper then failed to keep out a low free-kick from Luiz, who had earlier been cautioned for a poor challenge on Philipp Degen.