Callaspo, 23, lined a two-out single to right in the bottom of the eleventh inning to lead the Sidewinders to a 4-3 walk-off victory.
The late inning heroics by Tucson's sparkplug shortstop erased the stellar performance by Bees starter Kasey Olenberger, who outdueled the much-heralded Micah Owings through the first seven innings of Wednesday's contest.
The righty held the Sidewinders to just two hits in his finest start of the season, walking three. After making it through seven innings only twice in his first 24 appearances, he has now gone that deep in back-to-back efforts at the end of the year.
After both starters left, the Los Angeles Angels' triple-A squad looked to put it out of reach, plating two unearned runs in the top of the eighth thanks to a pair of errors by the Tucson shortstop.
But then, in the bottom of the frame, the Diamondbacks propspects snapped out of it and took advantage of a bullpen which has been the Bees' weak link all season.
Marcus Gwyn sandwiched a wild pitch around a walk, double and single before getting chased without ever recording an out.
The offense had nothing left to offer after the game was evened up and the Bees' final nine hitters went down in order while the game stretched into extra innings.
Greg Jones put up matching zeroes against Tucson, but when he was lifted to open the 11th, Matt Hensley was unable to equal his success. A one-out double and a walk two batters later set up Hensley's matchup with Callaspo, who knocked a 1-0 pitch through the infield to decide the game.
Steve Shell will likely toe the rubber for the Bees in game two, which will be at 6:30 on Thursday in Tucson.