Skippered by Jonny Gray, and with Adam Ashe and Mark Bennett starting, Scotland produced a fine display against a powerful England side.
Fly-half Tommy Allan put the Scots in front with an early penalty but the English were rewarded for their advantage in the scrum with a penalty try to lead 7-3 on the half hour mark.
But the Scots closed the gap with another Allan penalty to trail by a single point at the break.
Exeter’s Henry Slade extended the lead with a penalty before his club teammate Luke Cowan-Dickie sealed the win five minutes from time.