Sebastian Soria and Youssef Msakni put Michael Laudrup's side firmly in the driving seat of the tie, before Hassan Al Haydos pulled one back for the hosts in a frenetic first half.
The visitors took the lead in the 13th minute when to Vladimir Weiss's ball across the six-yard box found Soria unmarked in the box and the Uruguay-born forward made no mistake from point-blank range.
Soria spurned a glorious chance to double their lead on the 30 minute mark but could only find the side netting.
His miss didn't prove costly, as Msakni soon made it 2-0 when the Tunisian broke free and was one on one with Saad Al Sheeb in the Al Sadd goal and made no mistake with his finish.
To their credit, Al Sadd didn't drop their heads and soon afterwards their deficit was halved when Abdelkarim Hassan's long ball found Al Haydos, who slotted the ball into the net with a deft finish.
In the second half, Al Sadd continued to look for the equaliser and Hassan and Muriqui both went close in the opening exchanges of the second stanza.
Msakni spurned two glorious chances to restore their two-goal lead, and Lekhwiya have goalkeeper Amine Lecomte to thank that they still go into next week's second leg with the advantage, after the stopper Hassan's powerful free kick from 40 yards late into the match.