With net minder Peter Hirsch in fine form, The Elite League Champions took the lead on 33.44 with a powerplay goal, assisted by Brian Lee and Dan Carlson.
Hull hit back on 34.12 with a goal from Konstantin Kalmikov but on 47.19, Greg Chambers netted, assisted by Brad Cruickshank and Dan Carlson to give Coventry a first leg lead.
Tickets are available for the second leg at the Sky Dome on Sunday night. Face off is at 6pm.