Tsonga, a French crowd favorite, moved on to the second round with 1-6, 6-3, 6-2, 6-4 triumph over Russian Andrey Kuznetsov.
Tsonga's next opponent will be Germany's Cedrik-Marcel Stebe.
Del Potro, meanwhile, doused Spaniard Albert Montanes 6-2, 6-7 (5-7), 6-2, 6-1, and will next face Edouard Roger-Vasselin of France, who bested Vasek Pospisil of Canada 3-6, 6-3, 6-2, 6-2 Sunday.
Also notching a Day 1 win was former champion Juan Carlos Ferrero of Spain, who dispatched Frenchman Jonathan Dasnieres de Veigy 6-1, 6-4, 6-3.
No. 26 seed Andy Roddick of the United States fell to Frenchman Nicolas Mahut 6-3, 6-3, 4-6, 6-2, while 21st-seeded Croatian Marin Cilic got past Daniel Munoz-De La Nava of Spain 6-4, 6-4, 7-5.
Other first-round winners included 14th-seeded Fernando Verdasco of Spain, 18th-seeded Stanislas Wawrinka of Switzerland, Nicolas Devilder of France, Gilles Muller of Luxembourg, Spaniard Pablo Andujar and Fabio Fognini of Italy.
Swim Week Miami Beach 2014 [PHOTOS]