Simon was twice broken in the first set but recovered to break his opponent three times.
The Frenchman started strongly in the second set, breaking Kendrick's serve in the opening game, but the American broke back in the sixth before Simon took the tie-break 9-7.
Simon, a semifinalist at the Open 13 in Marseille and the Dubai Tennis Championships, fired four aces in the match while Kendrick had four double faults.
Paul Capdeville of Chile upset fifth-seeded David Nalbandian 6-2, 6-2.
Nalbandian, the 2002 and 2006 champion, was broken once in each set to lose in 52 minutes.
The Argentine, who won the Sydney International in January, had injured a hip at the Barcelona Open last month.
Sixth-seeded Mardy Fish of the United States ousted Russia's Teimuraz Gabashvili 6-3, 6-4.
Spain's Oscar Hernandez dropped a set before triumphing 7-5, 1-6, 7-5 over local favorite Rui Machado.
On the women's side, top-seeded Iveta Benesova of the Czech Republic edged Neuza Silva of Portugal 6-4, 5-7, 6-4.
The 29th-ranked Benesova improved to 15-11 this year.
Eighth-seeded Anna-Lena Groenefeld of Germany fought back to overcome France's Pauline Parmentier 1-6, 6-3, 7-6 (1), while Jarmila Groth of Slovakia also rallied to defeat Mathilde Johansson of France 1-6, 6-1, 6-1.
Germany's Kristina Barrois knocked out Portugal's Maria Joao Koehler 7-6 (4), 6-0.
Top-seed Cornet ousted at Barcelona
Dynamo seek first road win in New England
Djokovic and Murray reach 3rd round at Monte Carlo
