The France left-back netted on 22 minutes with a powerful angled shot from inside the box as Lyon made up for a surprise 2-0 defeat at Toulouse in Ligue 1 on Saturday.
Gerard Houllier's side will have the chance to win their first trophy of the season when they meet Bordeaux in the final on March 21 at the Stade de France.
Bordeaux qualified with a 2-1 win at Ligue 2 side Stade Reims on Tuesday.
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Lyon got off to a sluggish start with Le Mans playing some neat football before Abidal, who was perfectly set up by midfielder Florent Malouda, opened the scoring midway through the first half.
The visitors created several chances early in the second half through Stephane Sessegnon and Ismael Bangoura.
Lyon did not ease up with France right-back Anthony Reveillere hitting Yohann Pele's post in the 57th minute.
Le Mans were reduced to 10 men with nine minutes remaining when Gregory Cerdan was shown a red card for a second bookable offence.
The League Cup winners will qualify for next season's UEFA Cup.
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