Sutton netted in the 36th minute of Saturday's SPL clash at Fir Park after Martin Canning had held the striker as the home side capitalised on a dominant first-half display.
Jim McAlister missed a free header for Hamilton just after the break but Motherwell finished the match on top to leave Hamilton five points adrift at the foot of the Scottish Premier League.
Hamilton have not won in the league since triumphing at Fir Park in October and lacked a cutting edge with winger Dougie Imrie failing to shake off a knock.
Flavio Paixao came in along with midfielders James Chambers and Mark Carrington as Accies lined up with a 3-4-3 formation, although Gavin Skelton's role was almost exclusively to mark Jamie Murphy, who again played just off the front two of Sutton and Francis Jeffers.
Motherwell had not scored in the previous three Lanarkshire derbies and the visitors enjoyed the better of the scrappy early exchanges.
Paixao tried to catch Darren Randolph off his line from just inside the Motherwell half but the goalkeeper saved comfortably, and Jon Routledge soon looped a header just over Randolph's bar following a McAlister cross.
The hosts came close in the 12th minute when Sutton was inches away from making contact with Gavin Gunning's low centre across the six-yard box following a skilful run from the left-back.
Motherwell gradually pushed Accies back, enjoying long spells of possession, and began to create chances just before the half-hour mark.
Gunning headed Tom Hateley's corner just wide and Jeffers lost David Elebert in the box to head Ross Forbes' free-kick, but Tomas Cerny got down well to make a one-handed stop.
Motherwell took the lead thanks to a needless penalty-box foul by Canning.
The defender, who conceded a penalty on Hamilton's last visit to Fir Park, pulled Sutton just inside the area as the pair went for Keith Lasley's cross.
Sutton had his back to goal and little support but he gratefully accepted the gift by sending Cerny the wrong way.
Motherwell continued to press and Cerny made two more fine saves from Murphy's powerful low drive and a 20-yard free-kick from Forbes.
McAlister should have equalised 90 seconds after the restart when he escaped Stephen Craigan to meet Routledge's cross but headed well over from six yards.
Hamilton brought on all three substitutes before the 61st minute, with Gary McDonald, Ali Crawford and Nigel Hasselbaink on for Chambers, Carrington and Paixao.
The second half was proving a scrappier affair with the deteriorating pitch not helping the flow of the game.
Motherwell remained comfortable but Hasselbaink had a half-chance following some persistent play from Crawford, looping a shot over from 20 yards.
Chris Humphrey and Stevie Hammell came on for the hosts and the former was soon heavily involved, failing to lob Cerny from outside the box before setting up Sutton to head straight at the goalkeeper.
Crawford created another half-chance with 15 minutes left when his free-kick found Mark McLaughlin but the defender stabbed wide from eight yards.
But Accies failed to put Motherwell under pressure after that as Humphrey proved a good outlet for the hosts.
The winger helped set up two chances which Murphy could not convert before turning inside Skelton and firing over after a clever pass from the impressive Shaun Hutchinson.
Sutton curled just over after Hammell led another breakaway as Motherwell wrapped up the points.