The former ATP number seven currently ranked 28th took less than 90 minutes to dispatch the 82nd-ranked Matosevic in the opening round.
Gasquet was one of two French winners as qualifier Kenny De Schepper put out Portugal’s Gastao Elias 6-2, 2-6, 6-3 to move into a second-round meeting with Gasquet.
Spain’s Pablo Carreno Busta advanced over Constant Lestienne of France 6-3, 6-1.
Gasquet has played a pair of finals in Portugal, losing to Novak Djokovic in 2007 and Juan Martin del Potro in 2012.
Gasquet last took to a court on cement in Indian Wells on March 15, retiring with a herniated disc in his back against German Michael Berrer in the second round.
The 28-year-old improved to 11-4 on the season after his winning debut on clay.
“I’m feeling better, it’s as important for me to finish the match as win,” said Gasquet. “I’m feeling better than a week ago, I’m more confident with my body.
“I’m very happy with the way I won today. I had no pain, but recovery is a long process. I have nothing to lose and can only get better. I need to play as many matches as possible.
“I’m feeling good now, but I had this injury for three months last year and it came back this year.
“It’s in my head a bit, it’s tough to play right now without thinking about it.”
Gasquet finished with nine aces and three breaks of serve. He won the opening set in a tiebreaker and broke early to dominate the second set on the way to victory.
Matosevic saved match points and forced the seed to salvage a break point in the final game before Gasquet claimed the win.
Nick Kyrgios, the seventh seed who turned 20 on Monday, was awaiting his clay season start after a spring ankle injury, with the Australian starting against Spanish specialist Albert Ramos-Vinolas.