Montanes took a 4-0 lead in the opening set and saved the two break points he faced in the second set. Ebden had seven double-faults.
Tursunov did not face a break point while Nedovyesov dropped serve three times.
Mayer rallied past Croatian wild-card entry Borna Coric 4-6, 6-3, 6-4, while the sixth-seeded Mahut overcame French qualifier Martin Vaisse 6-7 (4), 6-3, 6-2.
Mathieu won the last nine games in his 2-6, 6-4, 6-0 win over compatriot Lucas Pouille.