The Foreurs, 2-1, advanced to Friday's semifinal with the marathon win that ended with Richard scoring on a breakaway at 1:15 of the second overtime.
The Oil Kings, 1-2, will either join the Foreurs in the semifinal for a rematch or face the host London Knights in a tiebreaker Thursday.
Pierre-Maxime Poudrier scored short-handed for the Foreurs with captain Samuel Henley and Shawn Ouellette-St-Amant also contributinhg a goal apiece for the Quebec Major Junior Hockey League champions.
Curtis Lazar had a goal and an assist for the Oil Kings. Henrik Samuelsson and Reid Petryk also scored for the Western Hockey League champions.
Val-d'Or was outshot 50-33, but the Foreurs hung around like a bad cold and twice tied the game after falling behind.
Foreurs goaltender Antoine Bibeau stopped 47 shots, including a penalty-shot attempt by Edgars Kulda in the first period.
Oil Kings goaltender Tristan Jarry made 29 saves in defeat in front of 8,745 fans that thinned out considerably by the start of the second overtime.
The host Knights and Guelph Storm conclude the preliminary round Wednesday in a clash of Ontario Hockey League rivals.
The Storm are already in Sunday's final with two wins, while the winless Knights need a victory to avoid elimination and get into a tiebreaker. The winner of Friday's semifinal meets the Storm for the championship.
Looking for a way to shake off a 6-3 loss to Guelph the night before, the Foreurs shaved their playoff beards Tuesday morning. They were slow out of the gates for the second game in a row, but were able to stay on Edmonton's heels largely because of Bibeau.
London happens to be the site of the longest game in Memorial Cup history. The Ottawa 67's downed the Kelowna Rockets 3-2 after 95 minutes 41 seconds in 2005.
Edmonton and Val-d'Or both came close to ending it in the first overtime. Petryk hit the post seconds after the puck dropped. Val-d'Or had an odd-man rush later in OT, but couldn't get a clean shot away. Foreurs defenceman Phil Pietroniro hit the crossbar with five minutes to go.
Henley deadlocked the game 3-3 at 15:49 of regulation off a drop pass from Richard. The captain slid a backhand by Jarry's pad.
Samuelsson restored Edmonton's lead at 5:46 of the third off a quick transition out of their end. Brent Pollock in the neutral zone dished to a charging Samuelsson and the Phoenix Coyotes prospect beat Bibeau stick side.
Val-d'Or's Poudrier pounced on a blue-line turnover by Edmonton defenceman Ashton Sautner and scored on a short-handed breakaway at 9:38 of the second period to make it 2-2.
The Foreurs halved the deficit when Ouellette-St-Amant redirected a Ryan Graves wrist shot from the high slot at 17:04 of the first period. Jarry got a piece of the puck, but not enough as it ticked off his glove.
Edmonton was up two goals after nine minutes and it would have been three had Bibeau not stopped left-winger Kulda on a penalty shot at 10:11. Foreurs left-winger Louick Marcotte had slashed Kulda on a breakaway.
It was Bibeau's second stop on a penalty shot in the tournament. The Toronto Maple Leafs prospect foiled London's Bo Horvat in the first game of the tournament.
The 2014 MasterCard Memorial Cup is 0-for-3 in penalty shots as Jarry denied London's Ryan Rupert on Sunday.
Lazar was a buzzsaw for Edmonton in the first period. The Ottawa Senators prospect scored his team's second power-play goal of the tournament at the nine-minute mark and worked hard in the trenches to generate the first goal at 6:22.
Lazar shook off defenders behind Val-d'Or's net and got a pass out front to Petryk for the 21-year-old's second of the tournament.
Foreurs defenceman Guillaume Gelinas did not play Tuesday. Assistant coach Mark Pietroniro said earlier in the day Gelinas suffered a "knee contusion" in Monday's collision with Guelph's Chadd Bauman.
Val-d'Or's top defenceman joined his teammates for warmup, but spent most of it standing beside the boards looking sore. Gelinas left the ice before his teammates did.
The Canadian Hockey League fined the host Knights $1,000 for criticizing the officials following Sunday's 5-2 loss to the Oil Kings.