Dawson (29 disposals, two goals) and Izak Rankine were standouts in the 19.14 (128) to 7.7 (49) victory on Saturday night at Adelaide Oval.
The Suns' seventh loss in a row was compounded by losing Will Graham to a shoulder dislocation.
Adelaide stalwart Rory Laird hurt an ankle, but the Crows moved to fourth on the ladder with Dawson and Rankine (31 disposals, one goal) dominant in midfield.
Josh Rachele booted three goals, all by the second minute mark of the second term, and Wayne Milera (22 disposals) made a triumphant return from a hamstring injury.
Adelaide's on-ballers Sam Berry and James Peatling were also instrumental with 10 clearances each, while veteran Taylor Walker kicked 5.4.
"What pleased us most, players and coaches, was just the discipline, the mental strength we showed to stick to it for an entire four-quarter performance," Crows coach Matthew Nicks said.
The 14th-placed Suns offered meek resistance, particularly when outscored 10 goals to two in the second and third quarters.
Brownlow Medal winner Matt Rowell (27 disposals) battled hard, Jed Walter booted three goals, and the Uwland brothers, Bodhi and Zeke, toiled in defence.
But Graham's shoulder issue came on a grim night for coach Damien Hardwick and his team.
"It was a capitulation after quarter-time," Hardwick said.
"We just got belted up around the ball ... contest-wise, we just got absolutely blown off the park."
There was no sign of the slide early when the Crows, courtesy of a pair of Rachele goals, took a five-point edge, 3.2 to 2.3 at quarter-time.
But Adelaide then accelerated with a match-defining burst of four consecutive goals to delight the 40,165-strong crowd.
After Rankine scored and Rachele kicked his third, Ben Keays dribbled accurately for a 24-point lead.
In the aftermath, Suns defender Mac Andrew was penalised for dissent, gifting Jake Soligo a goal - and Adelaide a 30-point lead.
Despite the ankle injury to triple club champion Laird, the home side held a 27-point halftime buffer, 7.8 to 3.5.
The Crows produced another burst, booting six goals to one in the third quarter as the Suns collectively crashed.
Adelaide were 60 points up at three-quarter time, before stalwart Walker iced the winning cake with four final-term goals himself.
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