Ollie Watkins put the Premier League outfit in front with an early header, before the lead was doubled by a well-executed John McGinn effort before the hour mark.
However, Lille were well worth their late goal from Bafode Diakite, with Villa fortunate to hold onto an advantage ahead of next week's second leg in France.
The opening 10 minutes of the contest produced very little entertainment, with both sides showing preference to remaining in their respective shapes in order to give nothing away.
Leny Yoro then proceeded to hand Villa an opening, going to ground too easily to try to a win a foul, but it only gifted Watkins the chance to run in-field and see a shot well blocked.
From the resulting set piece, Watkins saw a shot kept out by goalkeeper Lucas Chevalier, but the shot-stopper had no chance from the following corner, as Watkins found space at the back post to power a header into the far corner.
While Villa were on top, Lille had two chances up the other end, both through Edon Zhegrova. Although the first effort was comfortably saved by Emiliano Martinez, the Villa goalkeeper had to come out quickly to block the second attempt from closer to goal.
Martinez then needed to be alert to deny the marauding Diakite, who had broken forward from the back, as Lille served Villa a further warning of their qualities.
Villa responded through John McGinn teeing up Leon Bailey on the right-hand side of the area, only for the winger to cut inside and curl a shot marginally off target, before Martinez again came to the rescue at the other end to deny Jonathan David.
After the restart, Villa went on the offensive and almost doubled their lead through Bailey, who collected a neat knockdown from Watkins before forcing Chevalier into a smart stop down to his left.
Before the hour mark, Villa made their dominance at the start of the second half count through a wonderfully-crafted McGinn strike, with the ball finding its way from a short corner to the edge of the box where the Scot placed a first-time effort low into the bottom corner.
Moments later, Lille thought they had immediately halved the deficit through Gabriel Gudmundsson lashing a volley home at the back post, but the Swede was marginally offside.
The pressure continued to come from the visitors, with Hakon Arnar Haraldsson forcing a save from Martinez at the near post after meeting a corner.
Villa did respond to an extent, but it was not enough to discourage the visitors who finally halved the deficit when Diakite got across the front of the defender at the near post to divert a header into the far bottom corner.
As the game entered six minutes of stoppage time, Yusuf Yazici almost found the far top corner with a wonderful curling effort, with Lille not taking a backwards step in trying to find a leveller.
However, Villa were able to hold on, albeit unconvincingly, ahead of turning their attention to the second leg, which follows a meeting with Arsenal at the Emirates Stadium on Sunday.