Mathis survived temperatures approaching triple digits to seize a one-shot advantage over John Merrick, Kris Blanks, Kevin Kisner, Colt Knost and Robert Karlsson. Knost was the only player in the field not to suffer a bogey Thursday.
Neither the leader nor any of those tied for second has won on the tour, although Karlsson has 11 victories on the European circuit. Karlsson won last year's season-closing Dubai World Championship.
Those shooting a 67 at the TPC-Southwind course were Fabian Gomez and Keegan Bradley, whose first tour victory came two weeks ago at the Byron Nelson Classic. Bradley is trying to join Mark Wilson and Bubba Watson as the only multiple winners on the tour this year.
The Southwind course proved to be a difficult test for those taking part in the final tune-up for next week's U.S. Open.
"When you see 4-under is low after the morning, you recognize that there's something going on," Mathis said. "Whether it be pin placements or firmness of the greens or tricky wind. So you just try to be patient."
There were 32 players with a sub-par score after the first round, including world No. 2 and defending champion Lee Westwood at 69. John Daly also shot a 69, his first round in the 60s since February.
David Toms, who took two weeks off after a second-place finish at the Players Championship and a victory at the Colonial Invitation, returned to action with a 75.
Swim Week Miami Beach 2014 [PHOTOS]