Rene Girard's men trailed 2-0 on the half-hour mark courtesy of an early brace to Bengali Koita at the Stade Pierre-Mauroy, putting the third-placed Ligue 1 side on the canvas.
A quick response from Ronny Rodelin in the 33rd minute dragged Lille back into the contest, and two goals inside the final quarter-hour from Jonathan Delaplace and Nolan Roux looked to have saved face for the top-tier club.
However, Rodelin was hero-turned-villain when he got the final touch into his own net to make it 3-3, and send the match into an additional half-hour period.
After extra time ended goalless, Lille claimed the shootout 6-5 - with 11 consecutive spot kicks converted before Caen's Mathias Autret blinked and missed his chance to send the second division side out of the competition.
In the upset of the day, Cannes - a fourth-division side - upended Ligue 1 club Montpellier 1-0 after extra-time.
Belkacem Zobiri scored the winner on 119 minutes, to eliminate the side that saw off Paris Saint-Germain in the previous round.
Montpellier had the chance to take the lead, when Mbaye Niang took a penalty kick in the 102nd minute, but his effort struck the upright and was cleared to safety for Cannes.
In an all Ligue 2 clash, Angers recovered from deficits in both regulation and extra time to prevail 4-2 over league strugglers CA Bastia.
Stephane Moulin's Angers sit second in the French second tier, no less than 27 points clear of division cellar-dwellers CA Bastia.
But the visitors to Angers' Stade Jean Bouin surprised their more-fancied rivals, when Sunday Mba struck on 31 minutes.
Angers would equalise through Khaled Ayari on 57 minutes, and neither side could find a regulation-time winner.
Mba completed an impressive brace, when he put CA Bastia ahead in the 105th minute, and the away fans would have been dreaming of a quarter-final berth.
However, Charles Diers did not let CA Bastia even take their lead to the half-time break of the 30-minute period, and Mohamed Yattara and Jeremy Blayac added goals in the final seven minutes to avoid a shootout and send Angers into the last eight.
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