Gulbis was made to work hard to win a frenetic encounter 6-3 3-6 7-6 (7-3) at the ATP 250 hard-court event.
The fifth seed needed just one break of serve to clinch the first set and that came in the eighth game as the Latvian punctured Chardy's resistance to take the lead.
Frenchman Chardy battled back superbly in the second to force a decider and he continued to show resilience in the third as he responded immediately after losing serve to break back and force a tie-break.
However, that was where his challenge ended as Gulbis demonstrated his class to finally seal the triumph.
He is joined in the second round by Grigor Dimitrov, who overcame Romania's Marius Copil 6-3 6-4.
The Bulgarian, seeded seventh, was in superb form throughout, winning 76 per cent of points on his first serve as he completed the victory in one hour and 20 minutes.
American Jack Sock pulled off a surprise as he beat Australia's Bernard Tomic 6-4 6-2.
Sock broke Tomic twice to take the first set and he took that momentum into the second, racing into a 5-0 lead before wrapping things up with little difficulty.
Swedish qualifier Joachim Johansson gave the home fans something to cheer about as he demolished Colombia's Alejandro Falla 6-1 6-3 in just 54 minutes.
Elsewhere in the draw, Germany's Jan-Lennard Struff beat Sweden's Milos Sekulic 6-3 6-0, but his compatriot Nils Langer suffered a 7-6 (7-5) 6-3 defeat to Spain's Guillermo Garcia-Lopez.