Murray, seeded third, improved his career mark to 5-0 against Viktor Troicki with a 6-0, 6-3 victory. Murray lost only three points on serve -- one a double fault -- and nine overall in the first set and didn't face a break point.
The No. 4-seeded Tsonga marked his 27th birthday with a 6-2, 6-4 decision over Philipp Kohlschreiber. Tsonga fought off all six break points he faced on the day.
No. 13-seeded Fernando Verdasco got past Ivan Dodig 3-6, 6-3, 6-1 in the other second-round match Tuesday. Verdasco took 60 percent of the points in the final set.
Three seeded players were ousted in first-round matches. Stanislas Wawrinka stopped 10th-seeded Feliciano Lopez 6-1, 6-4 while qualifier Mikhail Kukushkin was a 3-6, 6-1, 6-3 winner over No. 14th-seeded Florian Mayer. Robin Haase advanced when 11th-seed Juan Monaco retired in the third set. Monaco, who won the U.S. Men's Clay Court Championship last week, was up 5-7, 6-0, 3-2 when he was unable to continue.
No. 12-seeded Kei Nishikori claimed a spot in the second round by beating Albert Ramos 6-2, 7-5.
Seppi's win puts him into a second-round match against world No. 1 Novak Djokovic.