Kevin Connauton also scored for Chicago (24-15-5) in the win.
Cedrick Desjardins made 36 saves for Hamilton (15-24-6) in a losing effort.
Chicago raced out to an early lead at 2:51 of the first, when Devin DiDiomete sent Davies in on a breakaway with a long, pinpoint pass through the middle and the forward moved to his backhand to elevate the puck above Desjardins' right shoulder.
If their first goal had been a thing of beauty, the Wolves' second was far from it.
The Vancouver Canucks affiliate doubled its lead less than a minute later when a wayward pass through the slot was corralled by Connauton along the boards and the defenceman released a speculative wrister that fooled Desjardins on the short side.
The Bulldogs enjoyed their best chance to score with 3:30 to play in the period, when Patrick Holland's backhand pass found a speeding Joey Tenute on the right wing, and the centre broke in alone on Climie. But the Chicago goaltender was equal to the challenge, dropping into a controlled butterfly to deny Tenute's wrister from close range.
The Wolves, much as they had in the first, struck quickly to open the second period, and it was Davies who provided the finish at 2:28.
He carried the puck over the Hamilton blue-line and decided to shoot upon hitting the top of the right circle, producing a wicked wrister that deflected off the crossbar above Desjardins' far shoulder and in.
The quiet second period was largely devoid of scoring chances at either end of the ice, but Hamilton threatened with two minutes to play.
Climie was rarely tested in Chicago's net, but denied the few scoring chances Hamilton did have in the third to preserve his third shutout of the season.
The Bulldogs enjoyed their most organized power play of the night two minutes into the period, and Mike Blunden forced a sharp pad save from Climie after receiving a centring pass in the slot.
More often than not, it was Hamilton's own inability to provide the final touch that kept it off the scoreboard.
The aforementioned Blunden was presented with a golden opportunity to score the Bulldogs' first goal with seven minutes to play, when he shed his defender and sped to the front of the net.
But the winger was unable to connect on the centring pass that followed, and smashed his stick on the ice in disgust when his shift came to an end.