Ryan Lollis and Eli Whiteside each walked to open the bottom of the 11th inning, and both were moved to third and second base, respectively, after Wilmin Rodriguez laid down a sacrifice bunt to set up Burriss' game-winning hit.
Rodriguez pitched a 1-2-3 top of the 11th inning to pick up the win. The left-hander benefitted from a diving catch by each Francisco Peguero and Lollis.
Wednesday's game was the fourth extra-inning game of the eight-game home stand and eighth extra-inning contest for Fresno since July 2nd. The Grizzlies will have their only off day of the second-half of the season on Thursday.
The Grizzlies wasted little time putting runners on the board as the first four batters in the Fresno lineup scored in the first inning. After Burriss walked and Justin Christian was hit by a pitch, Peguero hit a ground ball up the middle to score the first run.
Christian later scored on a wild pitch, and Nick Noonan hit a two-run single to the opposite field in left to give the Grizzlies a 4-0 lead.
Noonan added a two-run home run to right field for his third and fourth RBIs of the game.
A five-run inning by Memphis in the top of the fourth, however, turned the game into a one-run contest. Nick Derba's two-out, three-run home run to the left field bleachers capped the big inning and made it 6-5 Grizzlies.
The Redbirds tied it up at 6-6 in the sixth inning. Eugenio Velez led off the inning with a triple to the right field corner, and he was driven in by Nick Derba on a sacrifice fly to right field.
The 10th inning featured opportunities for both teams to score. Dan Runzler got Ryan Jackson to strike out for the fourth time in the game to end the top of the 10th inning. Jackson's strikeout came with runners on first and second.
Peguero, meanwhile, led off the bottom of the 10th inning with a double to the left field corner, but Memphis reliever John Gaub entered with Peguero on third base and ceased the runner in scoring position opportunity. Gaub got Gillaspie to ground out to short with the infield in and Noonan to pop out foul to end the frame.
The Grizzlies will make their first stop during the upcoming eight-game road trip in New Orleans to take on the Zephyrs. Right-hander Yusmeiro Petit will start for Fresno on Friday and face Elih Villanueva of New Orleans.