After a scrappy, goalless first half, Gills right-back Matt Fish broke the deadlock on 59 minutes after Sam Slocombe could only parry Chris Whelpdale's curling effort.
Deon Burton doubled the home side's advantage six minutes later, heading home Myles Weston's cross for his first FA Cup goal in seven years.
Substitute Danny Kedwell sealed the result from the spot on 76 minutes after Danny Jackman had been clumsily fouled by Josh Walker. Adam Birchall added a fourth for the Gills in stoppage time, bundling the ball over the line from close range.
With Laws watching from the sidelines, the visitors started the game brightly, and had the better of the early exchanges. Mike Grella forced Stuart Nelson into an early save, while Walker and Mark Duffy also threatened.
Connor Jennings should have given the Iron a late consolation, but the striker headed over from 10 yards.