Centeno led off the bottom of the 12th inning with his second double of the game before taking a seat in favor of McQueen.
After the Cyclones' James Schroeder dropped a sacrifice bunt to move the winning run to third base, the Jammers' Josh Hodges unleashed a wild pitch that allowed McQueen to cross the plate.
Brooklyn held a 6-3 lead after seven innings, but Jamestown plated four runs in the top of the eighth on consecutive singles by Harold Brantley, Pedro Mendoza, Marcell Ozuna and Ryan Fisher.
Darrell Ceciliani, who reached base five times for the Cyclones, scored on J.B. Brown's single in the eighth, and after both teams plated a run in the ninth, the game entered extra innings.
For Brooklyn, Joe Bonfe went 3-for-5 while scoring twice and William Cherry doubled, singled and drove in a pair.
Starter Angel Cuan yielded three runs on four hits and three walks while fanning five over seven innings. Ryan Fraser struck out five and yielded one hit over three scoreless frames before A.J. Pinera fanned two in a perfect 12th for the victory.
Ozuna finished 3-for-6 with a homer and Brent Keys doubled twice for the Jammers. Jamestown starter Jared Rogers allowed five runs on four hits over five innings.
The Cyclones, who lost Game 1 in Jamestown, 7-6, on Tuesday, will host the Jammers in the series finale at 7 p.m. ET on Thursday.
In other New York-Penn League action:
Batavia Muckdogs 5, Tri-City ValleyCats 4
Zach Russell overcame first-inning jitters to allow two runs on one hit and four walks over six frames as the Muckdogs edged the ValleyCats to even the semifinals, 1-1. Batavia's Jonathan Rodriguez went 3-for-4 with two RBIs and teammate Nick Longmire added a double and a single. Box score