Niger striker Maazou headed home with 10 minutes left in the extra period after Lens had dominated an entertaining game at the Stade Louis II.
Monaco will face amateurs Quevilly or Paris Saint-Germain, who play on Wednesday, in the May 1 final at the Stade de France.
It will be the third Cup final for Monaco coach Guy Lacombe, who lost last year's showpiece clash with Stade Rennes.
"I never had the chance to have a squad able to win the league but the cups are important," Lacombe told reporters. "Now we have to win that final."
"We suffered during the first half but we know that we always get opportunities to score, notably through Nene, who offered me the winning goal," said Maazou.
Lens were more aggressive in midfield but failed to convert two clear chances before the break through Kanga Akale.
The Ivory Coast winger missed the target after breaking down the left flank in the sixth minute.
Shortly after the half hour, Akale collected a defence-splitting pass from Yohan Demont but was denied from close range by Monaco keeper Stephane Ruffier.
Monaco earned a penalty 10 minutes into the second half when Alejandro Alonso was brought down in the box by keeper Vedran Runje.
Nene converted it but, with a few players in the box when he took his shot, referee Stephane Bre asked for the spot kick to be retaken and the Brazilian striker skied his second attempt.
With the match into extra time, Lens midfielder Sebastien Roudet had a clear chance in the 98th minute but his header was parried away by Ruffier.
One minute later, Maazou replaced Alonso and immediately made his presence felt when he headed home a Nene cross.
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