Stephenson later connected on two more kills, first a left-to-right, cross-court shot that preceded another hammering spike that Burbank libero Stefanie Lin was unable to dig.
The second kill put the Indians up, 20-10, and Burroughs breezed to a 25-14 match-clinching victory.
"It was so intense out there, I could barely catch my breathe," Stephenson said, as she led all scorers with 24 kills and three aces. "The nail-biters were the most intense, especially against a team like Burbank. We love to cream them."
Just as in the fourth game, Stephenson closed out Burroughs' thrilling 27-25 triumph in the third game with an ace.
The Indians appeared to have the game wrapped up after a Bulldogs' error put the visitors up 22-19.
However, Burbank battled back with a kill from Reilly Brennan, followed by an ace from Tyler Brooks, and eventually caught the Indians at 24.
Both teams traded a point until Burroughs scored the final two points on a kill from Tessa Dudley that was followed by Stephenson's ace.
The late heroics originally came from Burbank, as the Bulldogs became the first team to take a game from the Indians in league, winning the second game 28-26.
In that game, the Bulldogs trailed from the start but tied at 15 on two consecutive blocks from the tandem of Jaime Gonzalez and Stephanie Eskander on Stephenson.
Even so, Burroughs pushed Burbank to game point three times before the Bulldogs reversed the order and took a 27-26 advantage on a kill from Eskander.
Burbank then sealed its victory on an Indians' attacking error.
The error typified a frustrating day for the Indians, who surrendered 16 points via errors in the second game and overall committed 20 service errors in the match.
Other than Stephenson, the Indians received solid offensive efforts from Dudley (nine kills) and Laura Howard (four kills and an ace).
As for Burbank, Brennan led the way with six kills and a block, while Eskander added four kills and two blocks and Brooks contributed three aces.
"We played great in the first three games and lost it in the last game," Burbank Coach Sarah Brown said. "When you're not used to playing in these types of emotional games, it can be draining and it seemed like we ran out of steam."