Leon Osman, Phil Jagielka and Steven Naismith got on the scoresheet on as Roberto Martinez's men maintained their unbeaten record in the competition.
Everton have now picked up an impressive eight points from their four games, meaning they are one point clear of second-placed Wolfsburg and, more importantly, five ahead of Lille in third with just two group matches remaining.
The Premier League side's confidence on the continental stage was there for all to see in the first half, as Osman and Jagielka found the net.
Not content, Everton remained in the ascendancy and finished the job thanks to Steven Naismith's superb strike just after the hour mark to put themselves within touching distance of qualification for the last 32.
Everton got off to a strong start and almost took the lead when Romelu Lukaku's powerful drive was turned around the post by Vincent Enyeama.
That set the early tone for the game as Martinez's side dominated.
They should have earned their reward in the 15th minute, yet Naismith headed a golden chance over from Aiden McGeady's free-kick.
Scenting an opportunity to capitalise on their opponents' profligacy, Lille came back into the game - epitomised by Tim Howard being forced into a solid save to keep out Ryan Mendes' effort.
Yet that merely served to reawaken those hosts, who took the lead when Osman - selected as one of four changes from the weekend's goalless Premier League draw with Swansea - half-volleyed home after McGeady's right-wing cross had reached the back post.
Everton continued to press forward, with Lukaku heading just wide from the impressive McGeady's centre.
And Martinez's team grabbed a second just before half-time, Jagielka meeting McGeady's corner with an excellent diving header.
Lille controlled the ball in the early part of the second period, yet Everton almost grabbed a third when Enyeama produced a fine save to keep out Lukaku's 25-yard free-kick.
The hosts did not have to wait much longer to score again, however, as Naismith hammered Baines' cross into the roof of the net after a flowing team move also involving Lukaku.
Everton took their foot off the pedal thereafter, yet the ease and control with which they finished the game will have undoubtedly given Martinez more pleasure.
And in a moment that summed up Lille's evening on Merseyside, their best effort to get back into the match came in the 87th minute, when Franck Beria shot high and wide of Howard's goal from distance.
