Trailing 1-0 from the first leg played in Denmark, the French club won the second leg 2-0 in extra time at home.
Copenhagen made the brighter start of the two sides and created their first chance of the match on six minutes.
Cesar Santin skipped past Marko Basa and came in an one-on-one situation with Mickael Landreau, but failed to keep his shot on target.
A minute later Lille's Tulio De Melo headed over the visitors' goal from close range.
That was the start of the French club's domination of the first half that saw them come close on 18 minutes when Basa's diving header was nicely saved by Johan Wiland.
Two minutes later Wiland was forced to make another save, as he kept out Claudemir's deflection that would have seen the Danish side concede an own goal.
Rudi Garcia's men eventually broke the deadlock two minutes before the half-time interval.
Payet sent Salomon Kalou through, and the Ivorian attacker put a hopeful ball across the face of the Copenhagen goal that Lucas Digne slammed home with ease.
Ten minutes into the second half Lille could have conceded an own goal when Kalou almost headed a Copenhagen corner into his own goal.
The visitors from Denmark improved as the second period progressed and kept out Lille from scoring the second goal that would have seen them win the tie.
However, Lille had the last laugh when in extra time they found the Copenhagen net once again.
Nolan Roux was creator of the winner in the 105th minute when he curled in a cross that De Melo headed home.