Sutton struck twice in the first half hour as the visitors dominated, but a spirited second-half showing from County saw them reduce the deficit through Melvin De Leeuw. Despite Ross pushing hard for a leveller, Motherwell - beaten 5-0 by Celtic in their last league outing - held on for all three points.
After a slow start to the match it came to life in the 14th minute with a Richard Brittain free-kick which rattled the Motherwell crossbar.
But the visitors went straight up the field and took the lead with a deflected shot from Sutton which wrong-footed Michael Fraser on its way into the net.
The home side tried hard to get back on level terms but despite a fair amount of pressure they failed to test Motherwell's on-loan goalkeeper Dan Twardzik.
It got worse for County in the 27th minute when the visitors doubled their advantage. Henri Anier tried a speculative shot from well outside the area which was scooped away by Fraser but Sutton was on hand to steer the rebound home.
County boss Derek Adams made an early chance with forward Kevin Luckassen coming off the bench in place of holding player Marc Klok.
The change seemed to give County a much-needed lift and the substitute was soon in action with a near-post header from a Brittain cross which Twardzik did well to tip over.
The visitors threatened early in the second half when Lionel Ainsworth went on a 40-yard run down the right touchline and his cross into the box was deflected behind for a corner.
At the other end Ben Gordon went on a surging run before squaring the ball for Rocco Quinn, whose goalbound shot was smothered by Twardzik.
The home side looked more in the mood and Quinn had another chance in the 57th minute when he pounced on a De Leeuw flick-on but his shot was well wide.
Pressure paid off in the 61st minute when Luckassen won the ball near the corner flag and his deep cross to the far post was headed in from close range by De Leeuw.
The visitors had a let-off in the 67th minute when Brian McLean had the ball in the net following a Brittain corner but referee Crawford Allan blew for an infringement in the box.
County continued to press and they were almost in shortly afterwards when substitute Gary Glen and Brittain combined to set up Luckassen, whose shot was blocked at the back post by Twardzik.
With time running out there were chances at both ends.
Firstly Quinn forced another fine save from Twardzi, before Well raced up the pitch and Fraser did well to come off his line to thwart substitute Craig Moore.
County continued to push for a leveller but the visitors held out.