Djokovic manhandled Paolo Lorenzi 6-2, 6-0, 6-0. Djokovic had his serve broken in the match's third game but then ran off the next 17 games for the win. He won 67 percent of the points on serve and 69 percent when receiving. Djokovic took 22-of-29 points off Lorenzi's second serve.
Fourth-seeded Andy Murray, who lost to Djokovic in the 2011 Australian Open final, got by Ryan Harrison 4-6, 6-3, 6-4, 6-2 despite 40 unforced errors while No. 5-seeded David Ferrer beat Rui Machado 6-1, 6-4, 6-2 and sixth-seeded Jo-Wilfried Tsonga was a 6-4, 3-6, 6-3, 7-5 winner over Denis Istomin.
Gilles Simon, the No. 12 seed, had to go five sets before getting past Danai Udomchoke 6-1, 3-6, 6-7 (5-7), 6-3, 6-2 but No. 14 Gael Monfils and 15th-seeded Andy Roddick both advanced in straight sets.
Other seeded winners Tuesday were No. 17 Richard Gasquet, 19th-seeded Viktor Troicki, No. 23 Milos Raonic, No. 24 Kei Nishikori, 26th-seeded Marcel Granollers, No. 27 Juan Ignacio Chela and 32nd-seeded Alex Bogomolov Jr.
Unseeded players, in addition to Mahut, who moved into the second round were Lleyton Hewitt, Matthew Ebden, James Duckworth, Santiago Giraldo, Thomaz Bellucci, Tatsuma Ito, Julien Benneteau, Ryan Sweeting, Michael Llodra, Mikhail Kukushkin, Ricardo Mello, Andrey Golubev, Frederic Gil, Pablo Andujar, Philipp Petzschner and Edouard Roger-Vasselin.