Cam Zurhaar kicked six goals - including the match-winner with less than three minutes left - as the Kangaroos triumphed 14.8 (92) to 11.22 (88) at Marvel Stadium on Saturday.
It snapped a 14-match losing streak in Adams' first game in charge after taking the reins from David Noble.
The shock result was eerily similar to the Kangaroos' first game under Rhyce Shaw in 2019, when they upset flag-bound Richmond immediately following Brad Scott's exit.
It was a blow to the Tigers' finals hopes, leaving them clinging to eighth spot on percentage ahead of a clash with Fremantle in round 19.
There is doubt over Toby Nankervis' availability for that match after he was reported over an incident where he roughed up Flynn Perez, though there didn't appear to be much in it.
Zurhaar was the Kangaroos' hero in attack as Jy Simpkin (34 disposals), Luke Davies-Uniacke (28) and Hugh Greenwood (24) played integral roles in the midfield.
Ben McKay starred in defence and Paul Curtis (14 disposals, three goals) was also important.
Richmond had plenty of strong contributors through the middle - including Dion Prestia (26 disposals), Trent Cotchin and Jayden Short (24 each) - but let themselves down in front of goal.
Veteran spearhead Jack Riewoldt kicked 2.6 and third-gamer Noah Cumberland 3.4, with Riewoldt (twice), Noah Balta and Shai Bolton all missing chances in the final quarter of what could prove to be a costly loss.
Adams simplified North Melbourne's attacking plan and implored his players to express themselves by taking the game on.
It wasn't always pretty - Adams expected mistakes - but it led to the Kangaroos' highest score of the season.
Zurhaar had five goals from five kicks to half-time as the focal point, helping his side to a 32-point lead on the back of remarkable efficiency.
The Kangaroos' 10.2 (62) came from 23 forward entries, while Richmond had 3.12 (30) from 32 entries.
The margin was cut to 10 points by three-quarter time and memories of last round's big fade-out, when North Melbourne threw away a comfortable lead against Collingwood, no doubt haunted the Kangaroos.
Richmond hit the front when Jack Graham converted a free kick but Zurhaar responded when he gleefully accepted Todd Goldstein's expert hit-out at a boundary throw-in and snapped truly.
The Tigers had one last chance in the final minute when activated substitute Jake Aarts marked inside-50.
But Aarts played on and eventually saw a snap shot rushed through by North's desperate defence.
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