PSG goalkeeper Gregory Coupet, retiring at the end of the season, misjudged Obraniak's wide free-kick which drifted over his head and went in off the post after 89 minutes.
Coupet redeemed himself slightly by saving Mathieu Debuchy's penalty moments later but the damage had been done as Ligue 1 leaders Lille took their sixth French Cup. having last triumphed 56 years ago.
"At the end it went our way. It's 56 years that the people of Lille have been waiting for this," joyous coach Rudi Garcia told reporters.
"Now we are going to savour the win and prepare for Wednesday. Luckily we didn't have to play extra time. We know Ludo's left foot can cause damage, especially from dead ball situations."
PSG's only real sniff of a goal before the break was when Lille keeper Mikael Landreau was forced to save Nene's free kick with his legs and the second period brought even less goalmouth action for Antoine Kombouare's team.
"It's very tough," coach Kombouare said knowing his fourth-placed side host Lille again in the league next weekend.
"There is enormous disappointment for the players because they felt they had put in a good performance."
PSG, in six of the last nine finals including Saturday's clash, had veterans Claude Makelele and Ludovic Giuly in their team but not even their experience could help break down a Lille side who have prospered this term thanks to dogged hard work.
Winger Eden Hazard has often been the player to add the flair during Lille's surprise return to the upper echelons of French football but even he failed to shine on the day Inter Milan boss Leonardo denied reports his side have bid for the Belgian.
