Stansfield struck twice in the first half after Richard Logan had given an Exeter an early lead and they never looked back.
Gillingham looked brighter after the break but always lacked the firepower to trouble the well-organised Grecians.
Exeter took the lead with the first attack of the game in the seventh minute. Marcus Stewart found some space on the left and his perfect cross was headed home at close range by Logan.
Stewart volleyed wide after he was picked out by Logan and Stansfield was denied by the goalkeeper as the Grecians looked like increasing their advantage.
The second goal came six minutes before the break. Stewart picked out Ryan Harley inside the box and, when his shot was saved by Simon Royce, Stansfield was in the right place to stroke home the rebound.
Four minutes later Stansfield struck again. He pounced on a loose ball from John Nutter, sprinted into the box and stabbed the ball past Royce.
After the break Curtis Weston struck the ball over the bar for Gillingham and Andy Barcham curled an effort narrowly wide as the visitors chased the game.
Paul Jones then saved well from Albert Jarrett and Nutter struck the ball over the bar as Gillingham began to dominate. Jarrett then curled a free-kick inches past the post as the visitors desperately tried to cut the deficit.
But Exeter held firm and Harley had a close-range shot deflected past the post before Matt Taylor headed narrowly wide from a free-kick.
Gillingham had their best effort of the game in the closing stages when Jarrett stabbed the ball against the post with Jones beaten.