Goals from Cody McDonald, Joe Martin and Adam Barrett handed the Gills a thumping first victory of the season and lifted them off the foot of the League One table.
Martin Allen's side took the lead after 39 minutes courtesy of McDonald's third goal of the season.
The 27-year-old ran on to Charlie Lee's throughball down the left before calmly slipping his shot through Steve Phillips' legs.
After Danny Kedwell had spurned a chance just 10 seconds into the second half, Gillingham soon doubled their lead as Martin curled home a superb free-kick from 20 yards.
Substitute Vadaine Oliver had a couple of chances for Crewe as he forced Stuart Nelson into two excellent saves shortly after his introduction.
But Gills captain Barrett made the game safe and completed the scoring in the 70th minute when he smashed home from close range.