The match was the seventh since the Dreamtime at the 'G concept was established in 2005 with the Tigers' - 16.9 (105) to 13.11 (89) - win establishing a 4-3 lead overall.
The Bombers lost skipper Jobe Watson and Heath Hocking after last weekend's win over the Brisbane Lions and were without players of the calibre of Tayte Pears, Jason Winderlich and Michael Hurley; but they showed plenty of fight to be just 10 points down with 27 minutes played in the last quarter.
With both teams squandering chances in the desperately tense final minutes, Tyrone Vickery rose to the occasion and sealed a famous win with his third goal of the night.
Damien Hardwick demanded a greater defensive emphasis from his players after last weekend's shootout against the Western Bulldogs and the Tigers certainly obliged their coach in the first quarter.
James Hird did his best to stretch the young Richmond back six with David Hille, Paddy Ryder and Stewart Crameri all inside attacking 50, but the Bombers only managed to get it down to their tall timber nine times.
When they did, Alex Rance, Dylan Grimes and Luke McGuane were equal to the task more often than not.
A quarter played largely between the arcs produced two goals to each team, but the Tigers were able to take a one-point lead into a second term that was the polar opposite.
In this quarter the lead changed hands seven times with Essendon edging in front by a point at the main break.
Two goals to Jack Riewoldt helped Richmond bounce out to a 22-point lead at three-quarter time, which was a game-high at that point.
Nathan Foley's goal, after the Bombers pushed hard in the early minutes of the final term, edged the lead out to 23 points, but the brave Bombers agains closed, making the Tigers earn their fourth win of the season.
Richmond 2.3 6.5 13.8 16.9 (105)
Essendon 2.2 6.6 9.10 13.11 (89)
GOALS
Richmond: Riewoldt 4, King 3, Vickery 3, Nahas 2, Cotchin, Foley, Helbig, Newman
Essendon: Jetta 3, Monfries 3, Zaharakis 3, Crameri, Davey, Hille, Howlett
BEST
Richmond: Cotchin, Deledio, Martin, Newman, Nahas, Riewoldt
Essendon: Jetta, Heppell, Lonergan, Lovett-Murray, McVeigh, Hille
SUBSTITUTES
Richmond: Shane Tuck replaced by Mitch Farmer in the third quarter
Essendon: Kyle Reimers replaced by Alwyn Davey in the third quarter
Reports: Nil
Umpires: Stewart, Ryan, Jeffery
Official crowd: 83, 563 at the MCG
