The Crows lost star forward Riley Thilthorpe to illness before Friday night's match, but it mattered little as Adelaide kicked eight of the first nine goals to open up a 43-point lead midway through the second term.
West Coast fought back to close the margin to 18 points early in the final quarter, but two clutch goals to Ben Keays helped Adelaide see out the 15.9 (99) to 11.8 (74) win in front of 40,770 fans at Optus Stadium.
The result improved Adelaide's record to 10-6 ahead of next week's home clash with Gold Coast, while West Coast (4-12) have now lost four in a row.
Fogarty kicked three goals for the Crows in the opening term on the way to 4.0 for the match to go with seven marks, while Dawson (27 disposals, six clearances, one goal, 753m gained), Izak Rankine (27 disposals, seven clearances, one goal) and Keays (three goals) were prominent.
"We were looking for a strong start, and we were able to get that, which was really pleasing," Crows coach Matthew Nicks said.
"It turned into a bit of a slog, so to finish it off and get the win was a great result. We were able to hang on."
West Coast debutant Oliver Francou showed promise with 18 disposals, four clearances and nine tackles, while Jobe Shanahan and Jake Waterman kicked three goals apiece.
But the Eagles didn't get enough out of their stars, with Tim Kelly (19 disposals, two clearances) and Elliot Yeo (seven disposals, one clearance) below their best.
Adelaide dominated most of the key stats, but it was their ruthless first quarter that proved the ultimate difference.
Jake Soligo set the tone for Adelaide's dominant opening quarter, kicking a goal after just 17 seconds when he shook off a tackler and nailed his 49m shot on the run from near the boundary.
Fogarty monstered West Coast's defence to kick three goals for the term, with the only slip-up from Adelaide coming when Toby Murray fell over himself while attempting to collect the bouncing ball in his attacking goal square.
The quarter-time stats made for ugly reading for West Coast.
Adelaide dominated the inside 50m count (19-6), centre clearances (7-1) and contested possessions (44-29), resulting in a 38-9 lead on the scoreboard.
It was in stark contrast to a week earlier, when the Crows copped a pounding at the clearances on the way to a shock 26-point loss to Port Adelaide.
Fogarty kicked his fourth early in the second quarter as the lead ballooned to 43 points, but a smart dribble goal to Shanahan and a major to Willem Duursma got the margin back to 30 points by half-time.
Shanahan's two goals just before three-quarter time kept the Eagles within 30 points, and the margin was just 18 points with 17 minutes remaining after Bo Allan and Waterman nailed goals early in the final quarter.
West Coast tallied the first 13 inside 50s of the last term, but Dawson took some clutch defensive marks to help stem the tide and allow Adelaide to attack on the counter.
"We got blown away," Eagles coach Andrew McQualter said of the first quarter.
"The first 10 minutes of the game, they put four on us. In the past, that game gets a long way away from us.
"But the growth of our team is to fight, and we gave ourselves a chance to win that game, which is somewhat pleasing in that aspect, but we just can't give any team a lead like that."
