Falkirk 0 Motherwell 1
It gave the Fir Park outfit a useful win and exposed Falkirk's frailties at home as they have not won a home match in the league this season.
Falkirk should have taken more from the game but had nothing to show for sustained second-half pressure.
Alan Gow was not far away with an early header from an Andy Lawrie cross which dipped just over the top. But Motherwell hit back and were the more enterprising in the early stages.
Hamilton sent a couple of headers close before David Clarkson had the first clear-cut chance after 13 minutes. He skipped inside Tiago Rodrigues, but his shot was directly at Matt Glennon and, although the goalkeeper could not hold it, Falkirk managed to scramble the ball clear.
The Bairns fans felt they had a legitimate penalty claim midway through the first half when Craig McPherson's cross appeared to strike an arm, but referee Mike Ritchie was having none of it.
Falkirk came close shortly afterwards when Vitor Lima's 20-yard shot took a slight deflection which had Graeme Smith scrambling across goal, but it struck the side-netting.
The home side visibly improved after half-time. Russell Latapy dragged a shot inches wide of the post before Pedro Moutinho forced a great save from Smith.
It was Motherwell who took the lead after 59 minutes when Hamilton drifted off his marker at a Steve Hammell free-kick to guide a 16-yard header into the net.
Falkirk came back and a Latapy free-kick found Gow at the edge of the area, and he was just inches away with his left-foot shot.
Smith then saved well to keep out a header from substitute Daniel McBreen in the closing stages, but Motherwell held on for the three points.