Thistle went to Fir Park on a roll following a win and two draws in their first three games, but a second-half rally failed to yield an equaliser as Sutton's 21st-minute effort settled it.
The striker, who returned to Motherwell in the summer after two years at Hearts, scored the first goal of his second spell after Henri Anier and Zaine Francis-Angol combined to set him up.
Stephen McManus should have doubled the lead with a header, and Anier was then denied by Scott Fox's agility.
More home chances followed, Anier twice missing presentable openings and James McFadden heading too high moments after the restart.
A solo run from McFadden nearly brought a memorable goal, but Stuart McCall's decision to withdraw Anier appeared to give the visitors impetus and it was Partick who finished the stronger.
McManus saved Motherwell with a goal-line clearance and former Fir Park player Kallum Higginbotham saw a thumping shot blocked by Stevie Hammell as the hosts held on.