Gloucester were defeated by Exeter 22-10 in a thrilling contest. Exeter drew first blood as winger Mark Foster touched down in the fifth minute before James Simpson-Daniel hit back with a try for Gloucester.
Steenson hit three more penalties for an 11-point Exeter half-time lead.
Tim Taylor added a second Gloucester try but Steenson was unflappable and added six points to secure victory.
In front of 9,562 fans at Sandy Park, Exeter enjoyed the better of the opening exchanges and were rewarded for their early endeavour when Foster dived over.