Essendon's 10.11 (71) to 10.10 (70) win broke a 13-game losing streak against Richmond.
It also ends the Bombers' four-game losing sequence this season and breaks Richmond's run of eight Dreamtime wins.
The Bombers looked almost gone when Dustin Martin kicked a 50-metre bomb a minute into the last term to put Richmond 18 points ahead.
And Judson Clarke made the Bombers pay for another turnover, snapping a goal midway through the term to put the Tigers two goals up midway through the quarter.
But Essendon captain Zach Merrett was enormous, winning the Yiooken Trophy for best afield with a game-high 39 disposals, and he willed his team home.
Durham was playing for Richmond in the VFL two years ago when Essendon picked him up in the mid-season draft and he has never looked back.
Jake Stringer's snap found him at the top of the goal square in the frenetic last minute and he kicked the match-winner.
It was a high-pressure game, with a succession of fumbles.
Rhyan Mansell had a shot on goal for Richmond late in the last term but crucially it went out on the full and that kept the door open for Essendon.
Midfielder Dylan Shiel (ankle) was a late withdrawal in a major blow for the Bombers, who started slowly.
Richmond had the first seven inside 50s, but after Mansell kicked the opening goal at two minutes they failed to take advantage.
Two goals in as many minutes to Sam Weideman gave Essendon the lead and they took a two-point advantage into quarter-time.
The Bombers butchered their chances in the second term and a goal to Jack Graham before halftime gave Richmond a five-point lead.
Shai Bolton soccered an outstanding goal in the third term as the Tigers broke out to a game-high lead of two goals.
Martin's snap at the three-quarter time siren was touched on the line.
Richmond looked for much of the last term like they had a game-winning lead, with Essendon bombing the ball into attack and Richmond defenders mopping up easily.
But Durham's mark and goal at eight minutes kept the game alive and Stringer, virtually unsighted until then, goalled on the run to make it a one-goal contest.
After Clarke's goal at 17 minutes, Jye Menzie was on the end of an Essendon fast break to again reduce the margin to six points.
It became an arm wrestle until the last minute and Durham's match-winner - the only time Essendon led in the second half.
Martin and Bolton were best for Richmond, while Jordan Ridley impressed in defence for Essendon.