The Padres won for just the fourth time in 17 games.
Eckstein, who entered the game for defensive purposes in the top of the inning, lined a shot just past first baseman Josh Whitesell to bring in Kevin Kouzmanoff.
Kouzmanoff started the winning rally with a one-out double to left-center off Esmerling Vasquez, his third straight hit. Nick Hundley and Chris Burke, who was with Arizona last year, walked to load the bases and bring up Eckstein.
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Cla Meredith pitched a perfect 10th for the win.
After the game, the Arizona Diamondbacks fired Bob Melvin, hoping a new manager will be able to get the most out of their talented core of young players.
The 47-year-old Melvin's firing comes after a disappointing start by the Diamondbacks (12-17), who entered Thursday 8½ games behind the Los Angeles Dodgers in the NL West.
The 2007 NL Manager of the Year went 337-340 in four-plus seasons.
The Diamondbacks will name A.J. Hinch, their vice president for player development, as Melvin's replacement on Friday, according to a person familiar with the move who requested anonymity because the announcement had not been made.