Gaskins scored a career-high four touchdowns and Laub had career bests with 267 yards passing and two TDs.
Following an 83-minute rain delay, Gaskins scored on a 1-yard rush in the first quarter, a 5-yard rush and a 5-yard catch in the second and a 1-yard run in the third.
The Spiders (1-1), coming off a loss to Virginia, amassed 439 yards total offense while holding the Runnin' Bulldogs (0-2) to 247 in the schools' first meeting.
Laub was 14 of 24, including a 46-yard pass to Ben Edwards that capped a 17-point first quarter. He also threw one interception.
Richmond, under first-year coach Danny Rocco, won its eighth straight home opener.
Gardner-Webb, which scored on two field goals and a late safety, was led by Kenny Little with 75 yards on 13 carries.