Nadal, who cruised through his first two matches in Doha, was broken three times and finished the match with only 10 winners. Monfils had 35.
The 14th-ranked Frenchman also had eight aces to Nadal's zero.
Monfils will next face Andy Roddick in the semifinals. The eighth-ranked American defeated unseeded Victor Hanescu of Romania 6-3, 6-2.
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Roddick, Monfils through to 2nd round in Doha
