But a fairly comfortable win was tempered by injuries to first-choice goalkeeper Tomas Cerny and defender Mark McLaughlin, the latter of whom was taken from the field on a stretcher.
James McCarthy took his goals tally to four for the season, capping a sparkling performance from the 18-year-old.
For their part, Motherwell offered very little, with Chris Porter and John Sutton looking strangely toothless - although Porter did have a shot superbly touched over by Cerny in the first half.
But for a team that finished third last season, being ahead of bottom club Hamilton only via goal difference will be tough for their fans to take.
Hamilton should have taken the lead after five minutes when superb interchanging play between McCarthy and Richard Offiong sliced a path through to goal, but Offiong took a heavy touch, allowing Graeme Smith to gather.
A minute later, Porter went for a long ball and caught goalkeeper Cerny heavily and quite late.
When referee Iain Brines' attention was drawn to the situation, play was halted but the Czech star was eventually replaced by Sean Murdoch after 36 minutes.
Accies went close again in 25 minutes when Simon Mensing's corner was cleared only as far as McCarthy, who played a neat pass through Alex Neil to Offiong to dart through, but Smith blocked at his feet and the striker swiped a rebound over.
Paul Quinn had a shot on target after 33 minutes but his rising drive was straight at Cerny.
A minute later, Keith Lasley found Porter in the box and his shot on the turn was brilliantly touched over the bar by Cerny.
But Accies took the lead after 45 minutes when Mensing released McCarthy on the right, he beat the offside trap, steadied himself, and drilled an unstoppable shot past Smith and into the bottom left corner.
Accies could have doubled their lead two minutes into the second half when Offiong's knock-down on the right was volleyed over the top left corner by McCarthy.
After 49 minutes, Porter raced down the right and tried to set up partner Sutton for a tap-in, but Chris Swailes covered superbly to clear.
Hamilton wrapped up the points after 67 minutes when Mark Reynolds misjudged a long ball down the left and it fell straight into the path of McCarthy, who controlled on his chest before slicing the ball past Smith with the outside of his right boot.