Stevenson applied the two finishing touches but it was an accomplished team display that ultimately kept Hamilton, fourth in the Scottish Premiership table, at arm’s length.
Partick started on the front foot with Ali Crawford picking the ball up in midfield and riding a couple of challenges before shooting just wide.
Kallum Higginbotham’s powerful run won a corner which led to Stevenson’s first goal, with the 30-year-old reacting instantly to volley home after initially heading into the back of his marker at point-blank range.
Higginbotham should have doubled the lead soon after but wasted the opportunity by firing over the bar from close range.
Hamilton looked well off their normal passing rhythm and offered very little in the opposition half as Partick got to the break with their lead comfortably intact.
The second half was not much better from an Accies’ point of view and Stevenson made sure of the victory as he sidefooted home on 55, from inside the area, after being played in by Jake Carroll’s astute pass.
Hamilton were belatedly stung into action with Ziggy Gordon shooting over and Jesus Garcia Tena testing home keeper Paul Gallacher with a fierce free-kick, while Dougie Imrie was inches wide with a long-range drive.
But it was not to be for Hamilton, and their day ended on a low note as Imrie received a straight red card on 88 minutes for a scything challenge through the back of Carroll.