Salomon Kalou could have put Lille ahead after two minutes but the former Chelsea forward failed to hit the target with a header from close range.
Lille continued to have the better chances and Kalou was given an opportunity to make amends for his earlier miss when put through on goal but his shot was well saved by Johan Wiland.
The French side had an even better opportunity to take the lead when Kalou was fouled by Bryan Oviedo inside the box but Dimitri Payet's penalty was stopped by Wiland.
Copenhagen punished their opponents for their lack of clinical finishing when Santin headed past Mickael Landreau to give his side the lead.
Lille controlled the match in the second period but stubborn defending from Copenhagen prevented the French side's attacking players from creating clear opportunities.
However, it was Copenhagen who almost forced a late goal Martin Vingaard's free kick sailed just wide of the Lille goal and the Danish side finished the better of the two teams to hold on to their lead.