Scott Kelman had the Blaze ahead in the fifth minute with Danny Stewart adding a second seven minutes later.
Fifty two seconds in the second period and Paul Thompson's team were three goals up thanks to Jonathan Weaver netting from a Dan Carlson assist.
Basingstoke pulled one back but Barrie Moore fired home a fourth three minutes from time for another good win on the road.
Tomorrow night, Coventry Blaze are at home to Belfast Giants. Face off is at 6pm.