Cole Smith also scored, and Carter Hart made 20 saves for the Golden Knights, who are the No. 1 seed from the Pacific Division.
Vegas will play either the Montreal Canadiens or Carolina Hurricanes in the Cup Final. The Hurricanes lead that best-of-7 series 2-1.
Gabriel Landeskog scored, and Mackenzie Blackwood made 24 saves in his first start of the series for the Avalanche, who were the Presidents' Trophy winners.
Stone gave the Golden Knights a 1-0 lead at 4:42 of the first period. He gloved down a high flip from Brayden McNabb in the neutral zone, skated in on a breakaway, and used a backhand-to-forehand move to beat the left pad of Blackwood.
Stone had a goal and an assist in his return in Game 3, a 5-3 win on Sunday, after missing five games with a lower-body injury.
Smith extended the lead to 2-0 at 14:15 of the third period, redirecting Dylan Coghlan's shot from the point through Blackwood’s five-hole.
Landeskog cut it to 2-1 at 17:57 with Blackwood pulled for an extra attacker. He deflected Martin Necas’ shot from the point down off the ice and over the blocker of Hart.
Avalanche forward Valeri Nichushkin did not play because of a lower-body injury.
