In Perth, West Coast's finals hopes already look over after the Eagles crashed to a 0-4 record following a 37-point loss to Melbourne.
And over at Ikon Park, Carlton improved to a perfect 4-0 record with a 39-point win over Collingwood, 10.8 (68) to 4.5 (29).
Hawthorn entered Sunday's clash looking to start life at the Kennedy Community Centre with a win, but there were bad omens from the get-go.
During the warm-up, Jasmine Fleming was left with blood streaming from her nose after copping an accidental whack to the face.
Even though Fleming was able to return in time for the first bounce, the Hawks could only muster one goal in the first half as Adelaide entered the long break with a 34-point lead.
The Crows were never truly troubled on the way to the 10.7 (67) to 5.9 (39) win, with Hawthorn unable to play to their potential in Bates' milestone game.
Bates battled hard on the way to 28 disposals and three clearances, while Eliza West (27 possessions, nine clearances) and Aine McDonagh (three goals) were also prominent.
Fleming overcame her warm-up mishap to finish with 17 disposals and one goal assist.
But Adelaide's efficiency proved the difference, with the Crows' four-goal return in the opening term putting Hawthorn on the back foot from early on.
Crows star Ebony Marinoff fought through a tag on the way to 24 disposals, 13 tackles, four clearances and a goal, while Caitlin Gould and Chloe Brown kicked two goals apiece.
The result means both Hawthorn and Adelaide now have 2-2 records after four rounds.
Daisy Pearce's West Coast are still winless after falling to the Demons 12.9 (81) to 6.8 (44).
Eliza McNamara was electric for Melbourne with 33 disposals, two goals and 582m gained, while Tyla Hanks (29 possessions, seven clearances one goal) and Tayla Harris (13 disposals, 21 hitouts, two goals) also starred.
Gun midfielder Ella Roberts battled hard for West Coast with 26 disposals, nine clearances and 12 tackles.
But West Coast's latest loss means they will probably have to win seven of their remaining eight games if they are to repeat last year's maiden finals appearance.
Melbourne are 4-0 and loom as one of the main challengers to defending premiers North Melbourne (4-0).
At Ikon Park, Carlton kicked five goals to one in the third quarter against Collingwood to continue their unbeaten start to the season.
Ruby Schleicher was busy for Collingwood with 3.4 in front of goal to go with 12 disposals and 321m gained.
But Carlton had too much firepower, with three goals from Lila Keck and two apiece from Poppy Scholz and Erone Fitzpatrick lifting them to victory.
Mimi Hill tallied a game-high 31 disposals for Carlton, while Brittany Bonnici finished with 24 possessions and seven tackles for the Magpies, who slipped to 0-4 following on from last year's 3-9 return.
