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 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.
Archie 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.
"It's probably hard to separate the performance from the circumstance," Bombers coach Brad Scott said.
"We were just on the hop right from the start given we had to shuffle the deck chairs a fair bit.
"But probably the second half was where we thought we could get back into the game and we kicked 1.6 in the third quarter with reasonable control of the game.
"So it's obviously extremely disappointing not to get it done, and there's always (positives), but it's hard to talk about positives at the moment.
"We're in a situation that we don't want to be in and we've got to keep fighting."
Richmond improved to 2-9 and climbed off the bottom, but added another two players to their league-worst injury list, with tall forwards Tom Lynch (throat) and Jonty Faull (concussion) both hurt.
Lynch, who kicked two goals, including a crucial one early in the final term, was hurt before half-time.
But he played through pain and was taken to hospital for precautionary scans 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 important contributors.
"We set the tone and our leaders were terrific at the start of the game," Tigers coach Adem Yze said.
"We knew that we needed to start well - we didn't last week - and we knew we had a lot to play for.
"To see their attitude and intent in the first quarter, I just thought that we were going to fight our way through no matter what."
Darcy Parish (40 disposals, nine clearances), Zach Merrett (36, four) and Archie Roberts (33 touches) fought hard for Essendon, while 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.
