Mischa, seeded six, was beaten 6-7 (7-2) 7-6 (7-4) 7-5 by the experienced Spaniard Feliciano Lopez in a contest that lasted two hours and six minutes.
Lopez, who upset the third-seeded Tomas Berdych on Friday, will play his first final of the season as he bids for his sixth career title.
Benneteau failed to work a single break point against the promising star, who produced an utterly dominant display to set up a clash with Gilles Muller, a 6-3 3-6 6-4 victor against Aljaz Bedene.
"The match was so close from the beginning to the end".
In an all-French semifinal, the fourth-seeded Pouille beat Benoit Paire, 7-6 (5), 7-5.
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"I think my serve was working quite well in some important points, and that was probably something very important in today's match", Lopez said.
Berdych hit 21 aces to 19 for Lopez, but Lopez saved all nine break points against him on the grass court.
Hass, 39, handed his great friend Federer just a second defeat of the year on Wednesday, but could not follow it up as Zverev prevailed 6-4 6-4.
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