Uruguay striker Cavani netted twice in the first half, including a controversial penalty, to hand PSG their fourth League Cup title on a chilly night at the Stade de France.
Alexandre Lacazette reduced the arrears in the second half but Remi Garde's team could not find an equaliser.
Laurent Blanc's PSG team will now turn their attention towards claiming a second Ligue 1 title in succession as they hold a 10-point lead over AS Monaco with five games remaining.
Blanc claimed his side had put their Champions League quarter-final elimination by Chelsea behind them and the former France coach appeared to be right for a while.
Six days after losing 1-0 at Lyon in Ligue 1, PSG started the final by imposing their possession football on the game while their opponents sat back and waited to counter attack.
However, Lyon were forced to change their plans after four minutes when PSG scored their first goal in three games since striker Zlatan Ibrahimovic was ruled out with a thigh injury.
Cavani latched on to Maxwell's cross after the fullback was fed by Ezequiel Lavezzi's backheel on the edge of the box after a quick one-two between the Argentine and Brazilian on the left.
Cavani had another great chance in the 14th but his half volley from just outside the area was parried by Anthony Lopes.
Goalkeeper Lopes then fouled Lucas and referee Stephane Lannoy awarded PSG a penalty although TV replays showed the foul was committed outside the box.
Cavani converted the spot kick to double the tally in the 33rd minute and should have made it 3-0 minutes later from Lucas's perfect pass but he skied his attempt over the bar.
PSG played too casually after the break and were punished in the 56th minute when Lacazette beat Nicolas Douchez with low cross-shot from 18 metres after being let loose by Thiago Silva.
The goal put PSG on the back foot and Blanc made his first substitutions in the 74th minute when Yohan Cabaye and Javier Pastore came on for Marco Verratti and Lavezzi respectively.
The changes made little difference, however, with PSG seemingly happy to hold on to their slender advantage while Lyon lacked the creative inspiration to fashion an equaliser.
- Sports & Recreation
- Laurent Blanc
- Alexandre Lacazette
- Stade de France
- Ezequiel Lavezzi