The Gamecocks (4-3) also got a pair of touchdown passes from Dylan Thompson in putting away the Paladins (2-5), the defending Southern Conference champions who have lost five straight this season.
The win moved South Carolina coach Steve Spurrier to 51-0 all-time against teams outside the Power 5 or BCS-qualifying conferences.
Davis went over 100 yards for the third straight game and fourth time this season. His 5-yard TD run in the opening quarter broke a 7-all tie and put the Gamecocks ahead to stay. He added a 2-yard scoring run just before halftime for a 28-7 lead.
Thompson finished 14 of 22 for 262 yards, his highest total in four games since passing for 271 yards in a 38-35 win over Georgia on Sept. 13.
Backup runner David Williams had 110 yards in relief of Davis. It was the first time in seven years South Carolina's had two players rush for over 100 yards.
Hank McCloud had 106 yards rushing for Furman, including its lone touchdown as he outran South Carolina's defenders on a 60-yard burst. The Paladins managed just a Hunter Townes' 29-yard field goal the rest of the way.
The Gamecocks came in off a bye week, hoping to get back on track after two straight losses all but removed them from the SEC Eastern Division race. South Carolina coughed up a 13-point lead in the last 7 minutes of a 21-20 loss to Missouri before surrendering a 14-point margin in the final 12 minutes of a 45-38 defeat at Kentucky.
HBC coaching it up
Defensive coordinator Lorenzo Ward simplified his group's schemes and moved to the press box from the sidelines to more quickly identify adjustments.
The moves seemed to work. The Gamecocks forced a pair of fumbles — both which led to South Carolina touchdowns — and pushed Furman back after reaching the South Carolina 2. Townes missed a field goal to end the drive.
The Gamecocks allowed Furman 302 total yards, only 102 coming in the second half.
South Carolina's offense took charge early behind Thompson and Davis.
Furman came in leading the FCS in fewest passing yards allowed, but Thompson was comfortable and confident throwing from the pocket. He connected on TD passes of 14 yards to Shaq Roland and 45 yards to Jerrell Adams.
Davis, coming off a 183-yard, three-touchdown performance against Kentucky two weeks ago, continued that success against the Paladins. He had 81 yards and both his touchdowns in opening half.
Things will get much tougher when South Carolina returns to SEC play next week at No. 6 Auburn.
Furman has lost both meetings against South Carolina since 1982 when it shocked the Gamecocks at home 28-23. The Paladins received $250,000 for the matchup.