Acting skipper Tim Taranto and milestone man Jayden Short, in his 200th game, were influential in the Tigers' 10.14 (74) to 7.14 (56) victory at the MCG on Friday night.
Another huge crowd of 78,815 fans was on hand for the annual 'Dreamtime at the 'G' centrepiece of Sir Doug Nicholls Indigenous Round.
They witnessed a disaster for the Bombers (1-10), who lost skipper McGrath, Sam Durham (concussion) and Matt Guelfi (hamstring) to injuries before halftime.
McGrath took an accidental elbow to the mouth in the second term and was taken in an ambulance to hospital for treatment.
Archer May (ribs) was also taken to hospital and Jye Caldwell battled a leg injury.
A sixth-straight loss extended Essendon's worst start to a season in a decade and sent them to the bottom of the ladder.
The only downsides for Richmond (2-9) - already nursing the league's longest injury list - were injuries to Tom Lynch (throat) and Jonty Faull (concussion).
Lynch, who kicked two goals, was also taken to hospital after the match.
Taranto shone with 29 disposals and eight clearances, Short gathered 30 touches and a goal, while Patrick Retschko (27 possessions), Jack Ross (25) and Tyler Sonsie (21) were all busy.
Darcy Parish (40 disposals, nine clearances), Zach Merrett (36, four) and Archie Roberts (33 touches) fought hard for Essendon, while Archer May (three) and Nate Caddy (two) both kicked multiple goals.
Parish won the Yiooken Award as best afield and was jeered by Richmond supporters when accepting his prize.
Caddy had Bombers fans on their feet when he kicked their first goal and set up the second after a one-handed mark.
But they lost Durham and Guelfi in the opening stages, and Richmond led 4.5 to 2.2 at quarter-time.
Mykelti Lefau's soccer-inspired goal was the highlight of an even second term and Short sparked Tigers celebrations when he slotted the first major after halftime.
The margin reached a game-high 22 points but an inaccurate Essendon dominated territory for the third quarter, booting 1.6 to 1.3 as May's third major helped them get back with two straight kicks by the final change.
Jye Caldwell cut the deficit further and there was a controversial moment when Archer Day-Wicks slid to rush a behind on the goal-line and took out Green's legs, but was not penalised.
It didn't matter as Lynch converted a set shot moments later to give Richmond breathing space and second-gamer Noah Roberts-Thomson kicked the sealer in time-on.
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