Baker, on the run from a tight angle, slotted the match-winner in the Dogs' gallant 14.10 (94) to 13.10 (88) victory at Adelaide Oval on Friday night.
Luke Beveridge's side have now claimed the scalps of the reigning premiers Brisbane, last year's finalists GWS, and minor premiers Adelaide in a hot start to the season.
"I'll take a win any day of the week," Beveridge said.
"Most of the night we defended pretty well and we kicked a pretty good score.
"It's pretty encouraging."
But they required Baker's last-gasp heroics after comeback Crow Izak Rankine seemingly capped a stunning Adelaide fightback.
Adelaide appeared done when 26 points adrift early in the final quarter, but booted five goals in a 10-minute patch to snatch the lead.
Rankine, on return from a four-game ban for a homophoblic slur, sensationally put the Crows in front by six points with about eight minutes remaining with an eye-catching 47-metre goal on the turn.
But the Dogs, with Bailey Williams snapping accurately, squared scores, followed by Baker's brilliant late major.
Baker (three goals) was running at pace under severe heat but curled through the game-breaker.
His teammates Aaron Naughton and the dynamic Joel Freijah (24 disposals) also booted three goals each, while skipper Marcus Bontempelli collected a match-high 30 touches plus a goal.
Midfielders Ed Richards (29 disposals), Tom Liberatore (28) and Matt Kennedy (27) were all pivotal in the triumph.
Adelaide attackers Taylor Walker (three goals), Riley Thilthorpe (two), Darcy Fogarty (two) and Josh Rachele (two) all hit the scoreboard.
Captain Jordan Dawson (25 possessions, one goal) and Josh Worrell (25, nine marks) were also prominent.
"We were a bit slow to get going ... we left it too late," Crows coach Matthew Nicks said.
The Dogs, after consecutive conversions from Freijah following frees, set the tone early, racing to a 20-0 advantage.
Adelaide's first score came from a 50m penalty to Jordan Butts - his first goal in 87 AFL games - and the Dogs led 3.4 (22) to 3.0 (18) at quarter-time.
That advantage disappeared when Adelaide's Thilthorpe goaled to give the home side the lead for the first time.
However, it proved short-lived, the Bulldogs rising to the challenge in style as Freijah's third triggered the next four goals in a 15-minute burst.
The Dogs were 15 points up at halftime and both teams booted three goals before a third-term flashpoint when Sam Darcy gave away successive 50m penalties to Adelaide's Butts.
But the backman sprayed a 20m set shot that could have reduced the margin to only nine points.
Instead, to compound his blunder, Butts soon gave away a free kick to Darcy, who coolly converted a 50m shot for a 19-point buffer.
The home side scored another point, with the visitors taking an 18-point break into the last change, 11.7 (73) to 8.7 (55).
Naughton's third major increased the break to a seemingly safe 26 points, before Adelaide's late onslaught.Â
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