The Tigers, who lost the round nine 'Dreamtime at the G' clash between the two sides, withstood a late charge by the Bombers to win 15.11 (101) to 14.12 (96).
Richmond led by 29 points in the second term but allowed the Bombers to hit the front in the third quarter.
They moved four goals clear again early in the final term, but Essendon kept coming and kicked the last three of the game to ensure a cliff-hanger ending.
The ball ended in the Bombers' attacking half after young Tiger Shane Edwards took a match-saving mark with 10 seconds remaining.
Essendon's top-eight spot is now in serious jeopardy,
The loss leaves it one game behind seventh-placed Carlton and in direct competition with Port Adelaide and Hawthorn for that cherished eighth position.
Adding to the Dons' woes is the fitness of Matthew Lloyd, with the skipper spending the final term on the bench icing an injured ankle.
The Tigers have their own injury concerns after young defender Jarrod Silvester was carried from the field in the fourth quarter with a knee problem and skipper Chris Newman also leaving the arena with a knee injury just before the final siren.
Jack Riewoldt was the primary goalkicker for the Tigers with a career-best return of 6.1.
He was supported by an outstanding performance from Ben Cousins, who led the side with 31 possessions and a passionate half-time address.
Trent Cotchin was very impressive with 23 touches and six tackles, while Robbie Nahas again provided glimpses of excitement. Daniel Jackson was also influential with seven tackles and seven clearances.
For Essendon, Andrew Welsh fought hard in an engaging battle with Brett Deledio for 25 disposals, while Brent Prismall showed good signs in his seventh game for the club with 34.
Paddy Ryder was again excellent in a variety of roles, and Andrew Lovett gave the side speed and a much-needed pair of goals in the third term.
Cousins started exceptionally well for Richmond, and went berserk in the first quarter after the Bombers failed to designate a consistent run-with player for the Brownlow medallist.
He had 12 possessions in the low-scoring term, which the Tigers won by two points. Dean Polo was also picking up plenty of it, while an agitated Welsh was winning his battle with Deledio while helping himself to eight touches.
When Ryder out-tapped Tyrone Vickery deep in the Bombers' attack two minutes into the second, Jason Winderlich roved and goaled to force the fourth lead change of the game.
A follow-up goal to Riewoldt after a clever handpass by Nahas grabbed the lead back and this time it was for a significant period.
The Tigers kicked the next four to move out to a 29-point lead, with Cotchin and Nahas having plenty of influence over the assault.
A late flurry by the Bombers saved them from being pushed from the contest before half time. Ryder goaled after some skilful work by Winderlich, before Adam McPhee booted one shortly before the siren to narrow the gap to 16 points.
Two unanswered goals early in the third had Essendon within three points. After a major to Jackson and a spate of sprayed kicks, the Bombers reared again with Lovett's two goals in three minutes handing them the lead.
Kyle Reimers pushed his side six points in front with a goal at the 20-minute mark, but the Tigers finally kicked into gear and began to answer the challenge.
Riewoldt snared another two for the quarter while Jayden Post kicked his first AFL goal. Despite Nathan Brown – in his first game since round 10 – missing a sitter right before the siren, the Tigers had a 12-point lead at three-quarter time.
In the fourth, the Bombers kicked 4.3 to 3.2, but it wasn't enough to win the game.
Essendon will now meet West Coast at Subiaco on Sunday while Richmond will play Melbourne at the MCG earlier that day.
Essendon 2.5 5.6 10.9 14.12 (96)
Richmond 3.2 8.4 12.9 15.11 (101)
GOALS
Essendon: Lovett 2, Lucas 2, Reimers 2, Ryder 2, McVeigh, Winderlich, McPhee, Dyson, Dempsey, Stanton
Richmond: Riewoldt 6, Post 2, Morton 2, King, White, Brown, Deledio, Jackson
BEST
Essendon: Welsh, Prismall, Ryder, Lovett, Stanton, Winderlich, Fletcher
Richmond: Riewoldt, Cousins, Cotchin, Nahas, Deledio, Jackson
INJURIES
Essendon: Lloyd (ankle)
Richmond: Silvester (leg), Newman (knee)
Reports: Nil
Umpires: Donlon, McBurney, Hendrie
Official crowd: 47,412 at the MCG
The views in this story are those of the author and not necessarily those of the clubs or the AFL.
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