Nadal, reigning Wimbledon, French Open and Olympic champion, beat Belgian Christophe Rochus 6-0, 6-2, 6-2. The five-time major champion Nadal will face Croat Roko Karanusic in the second round.
Murray was leading Romanian veteran Andrei Pavel 6-2, 3-1 when Pavel retired due to back problems after 45 minutes of tennis. Murray is trying to become the first male player from Great Britain to win a Grand Slam tournament since Fred Perry captured Wimbledon and the U.S. Open in 1936.
Murray was a champion in Doha two weeks ago and reached the final at the last major event, the 2008 U.S. Open. Following Tuesday's match, Pavel announced his retirement from professional tennis due to his ongoing back problems.
Fifth-seeded Tsonga beat Argentina's Juan Monaco 6-4, 6-4, 6-0. Tsonga lost to Novak Djokovic in last year's finale here.
Former world No. 1 Lleyton Hewitt lost to 13th-seeded Fernando Gonzalez, 5-7, 6-2, 6-2, 3-6, 6-3, falling in the first round of the Australian Open for the first time since 2002.