Henne played the majority of the contest and was 15-of-24, while Matt Moore ended 6-of-10 for 73 yards for the Dolphins, who topped Atlanta last week.
Cam Newton went 7-of-14 for 66 yards in the first half for the Panthers, who won 20-10 over NYG to open their exhibition slate.
The Dolphins were in control from the start, as Hilliard's one-yard plunge was the lone score of the opening period.
Carpenter hit from 39 yards out and Thomas added a four-yard touchdown scamper for a 17-0 bulge at the break.
Carpenter connected from 44 yards out in the third quarter, before Carolina finally tallied in the fourth thanks to Adi Kunalic's 38-yard make and Sutton's four-yard TD run.