Tomic, 19, bested left-handed German qualifier Michael Berrer 6-3, 3-6, 6-3 at Rexall Centre, and moved on the second round where he will face defending Rogers Cup champion and world No. 2 Novak Djokovic.
Chardy, meanwhile, needed three sets to advance, getting past American Donald Young 3-6, 7-6 (7-4), 6-0.
Also Monday, Serbia's Viktor Troicki dispatched Russian Alex Bogomolov Jr. 6-4, 7-6 (7-5) and lucky-loser Matthew Ebden rallied to defeat Canadian wild card Peter Polansky 0-6, 6-4, 6-3.
Swim Week Miami Beach 2014 [PHOTOS]