The Tigers booted the final five goals of Saturday's game at the MCG, keeping the Hawks goal-less in the fourth quarter in a vital result for their flickering finals chances.
Richmond led early in the second quarter but didn't hit the front again until a minute remaining when Baker snapped his second goal to the huge roar of the Tigers faithful.
Hawthorn pushed forward from the next centre clearance but Richmond were able to thwart the Hawks' attack to prevail 14.12 (96) to 15.5 (95).
After being poor for much of the afternoon, Richmond's stars stepped up as Dustin Martin (two goals, 24 disposals) and Tim Taranto (three goals, 23 disposals) all played crucial roles in the final quarter charge.
Richmond were staring down the barrel of finishing the round as low as 14th had they lost, but the comeback means they have jumped back into seventh on the ladder.
The Tigers will likely need to win only three of their remaining five matches to be guaranteed of playing finals, with tricky games against the Western Bulldogs, St Kilda and Port Adelaide following next week's clash with Melbourne.
Sam Mitchell's Hawks shocked the Tigers with a brave and bold style of play, blowing the match open with six straight goals in the second quarter.
It seemed to be Hawthorn's day when Chad Wingard soccered the ball from near the boundary and it kept rolling through for an unlikely goal in the second quarter.
At the other end, triple Richmond premiership captain Trent Cotchin missed two shots from inside 15m directly in front.
In an added blow for Hawthorn after the heartbreaking defeat, they will potentially be without Ned Reeves for next week's match against St Kilda after he was reported for a dangerous tackle (rough conduct) on opposing big man Ivan Soldo.
The incident appeared to be even more severe than some of the tackles that have led to players being suspended this year under the AFL's crackdown
Another concern for the Hawks was former No.6 draft pick Denver Grainger-Barras failing to pick up a possession in two-and-a-half quarters before he was tactically substituted out in the third term.
Grainger-Barras spent 11 weeks out of the team but was recalled two weeks ago for the clash with GWS.
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