Humbert went out in the first round last year to Italian wildcard Lorenzo Sonego and, after losing the first set to Argentine Coria, the French 14th seed looked in trouble again.
He overcame the setback though and strolled to win the next two sets, breaking Coria's serve twice in each set.
Karen Khachanov was also made to battle before overcoming Britain's Cameron Norrie 7-5, 7-6(3). The Russian 15th seed had his serve broken twice in the opening set and was forced into a tiebreak in the second.
Norrie again broke serve twice in the second and at 6-5 up had two break points to win the set but Khachanov hit back with three consecutive aces to hold serve and fired another two aces to take the tiebreak with ease.
Khachanov will face Argentine Francisco Cerundolo in the second round.
Bulgarian ninth seed Grigor Dimitrov, who recently lost the Miami Open final to Jannik Sinner, came through his first round match with local wildcard Valentin Vacherot 7-5, 6-2.
Dimitrov, who won his first ATP title in over six years at the Brisbane International in January, was pushed hard in the first set with Vacherot breaking serve in the opening game, but found his groove to ease to victory in the second set.
"I'm just grateful that I was able to get through the match today like that. I know I'm far away from my game right now, but hopefully this is a build-up for me," Dimitrov said.
Twice Monte Carlo champion Stefanos Tsitsipas is also through to the second round after his opponent Laslo Djere retired injured in the second set. Tsitsipas won the opening set 6-3 and was 3-2 up when the Serb announced his withdrawal.
"I didn't expect such a finish. This is not something very common when I play," Greek 12th seed Tsitsipas said.
"I did my job well, and obviously, I'm wishing (Djere) a speedy recovery, because injuries are not fun."
The top eight seeds received byes to the second round, and Tuesday will see world number one Novak Djokovic in action against Russia's Roman Safiullin.
