Murray returned to the court for the first time since he cited a back problem as the reason for pulling out on the eve of last week's event in Basle.
The US Open champion moved freely in his second-round match as he was at times made to sweat before eventually overpowering his 30-year-old French rival 7-5 6-3 in one hour 33 minutes.
Mathieu, a wildcard entrant, pushed Murray throughout the opening set, but succumbed thereafter before conceding the match with a double fault.
"I felt okay. I served pretty well, but I struggled a bit on the return especially at the beginning of the match," Murray told Sky Sports 2.
"It's hard to say (how long it will take to return to full match sharpness). I've been playing very well in practice and felt confident today, but when the match started it's different conditions.
"I struggled with my timing. I've never played my best tennis at this tournament, but I'd like to change that.
"You'd hope after three or four matches you are starting to play better."
Murray will next meet qualifier Jerzy Janowicz, who he beat in the Davis Cup a couple of years ago, after the Pole upset 13th seed Marin Cilic yesterday [Wednesday].
That will come as a relief to Murray who was solid rather than spectacular in his first match since losing the final in Shanghai to Novak Djokovic at the start of the month.
He was forced to battle in a competitive opening set that lasted just shy of an hour.
The Scot was frustrated in the opening exchanges as Mathieu looked the more comfortable in reaching 5-5. But with the set on the line Murray found an extra gear at the right time.
After breaking Mathieu to love to make it 6-5, he was still made to sweat for the set as the Frenchman grabbed a couple of break-back points.
Murray coolly averted the danger, however, firing down and ace before Mathieu bunted a second serve long, to allow the world number three to close the set out soon afterwards.
After keeping pace with Murray for the best part of an hour Mathieu started to lose his way as he was immediately broken in the second set.
Murray's passing shot was initially called long but, after asking for a replay, he was handed the opening game before a second break made it 4-1.
Mathieu briefly threatened a comeback when he pulled back a break but Murray stepped it up again to go through.