Sutton made no mistake from close range after a sweeping move from right to left ended with Richard Butler served up a perfect cross for the striker to fire home.
And it proved enough to ensure that the Don Hill Memorial Trophy remains in the Moat Ground trophy cabinet for another year.
Gresley started with a strong breeze behind them and looked the more cohesive of the two teams, against a Romans side featuring six new arrivals in the starting XI.
Rocester, however, had their chances and should have done better on two or three occasions in the first half.
Just eight minutes into the game Luke Chapman's deft flick created an opening for Connor Bird which the youngster lofted high over the bar.
Shortly afterwards, Jack Langston's first-time effort from 20 yards curled away from goalkeeper Gary Hateley's left-hand post.
Chapman then spurned a decent opportunity to level things up when he got away from his marker only to miscue his low shot wide of the far post.
At the other end, Romans keeper Richard Froggatt was kept occupied by a lively Gresley attack, making two smart saves to deny Sutton and then Royce Turville as the dangerous Brian Woodall teased the home defence open with some neat footwork around the area.
The entertainment continued after the break with Rocester, in search of an equaliser, taking their turn with the favourable conditions.
They should have found the net when Ashley Justin ghosted in to meet a corner at the far post only to send his downward header narrowly wide.
Then, in the 69th minute, Mark Hodson forced a fine save from Hateley with a header from Craig Hulme's right-wing cross that was on its way into the bottom left corner.
Woodall had two bites at the cherry to double Gresley's lead on 76 minutes after substitute Micky Lyons had cleverly set him up, but Froggatt was equal to the first effort and Woodall's follow-up was scrambled away, as was Sutton's effort in the closing stages.
Rocester are back in pre-season friendly action tomorrow when they travel to Stafford Town. Kick-off is 3pm.
ROMANS: Froggatt; Price; Lowe; Wain; Justin; Bennett; Dacres; Langston; Chapman; Bird; Holt. Subs: Hodson; Hulme; Gough; Fleming; Roberts.