Mayer topped Gilles Muller 7-6 (7-3), 6-3 by cashing in the only two service breaks of the match. Muller won 77 percent of the points on serve but Mayer twice broke Muller's serve in the second set for the win.
Mayer landed 70 percent of his first serves and claimed 74 percent of the overall points when he served. He fought off seven break points in the first set in getting to the tiebreaker.
French players went 1-1 Monday.
Guillaume Rufin got past Vasek Pospisil 6-4, 7-6 (8-6) by recording the only break of the match to take the first set and then winning the close tiebreaker.
Nikolay Davydenko, however, ousted Rufin's countryman Stephane Robert 6-2, 6-1 in 59 minutes. Davydenko lost only five points on serve and won all 12 of his service points in the second set.
He moves into the second round against fourth-seeded Richard Gasquet, another French player. Gasquet and the other Top Four seeds, including No. 1-seed Tomas Berdych, received first-round byes.
No. 3-seeded Gael Monfils won the tournament in 2010 but it wasn't contested in 2011.