Matosevic, a qualifier, defeated Gasquet 1-6, 7-6 (7-5), 7-6 (7-3) in a second-round match that took 2 1/2 hours.
Gasquet dropped serve just once, falling behind 5-4 in the third set, but answered with a break of his own to even the match. Matosevic, however, grabbed the early advantage in the tiebreaker and held on for the victory.
The other matches Tuesday were all first-rounders, including Lu Yen-Hsun's 6-3, 2-6, 7-6 (7-4) upset of fifth-seeded Julien Benneteau. No. 6-seeded Andy Roddick, 7-11 this year, advanced when fellow American Sam Querrey retired after Roddick went up 5-2.
No. 7-seeded Philipp Kohlschreiber defeated Go Soeda 6-4, 7-5 and Denis Istomin was a 6-4, 6-3 winner over Michael Llodra in Tuesday's other matches.
2014: The Year in Music [PHOTOS]