Russell, the A's No. 1 prospect, led off the sixth inning with a single and stole second base. After Culver walked the bases loaded, Steven Souza delivered a two-run single to give the Solar Sox the lead.
Russell said the mindset of the Solar Sox hitters keeps them ready to break out in any inning.
"Really, no matter what happens, we look forward to the next pitch, the next at bat, the next big moment," Russell said. "We're all prepared for next big moment."
Russell has had a few big moments already in his first full professional season. The 19-year-old began the season at Class A Advanced Stockton, where he hit .275 with 17 home runs in 107 games. He ended his season with a promotion to Triple-A Sacramento for a late playoff push.
After a few weeks to rest at home, Russell came to the AFL. He said he didn't really know what to expect, but has found a good place to play.
"It's just a laid-back, relaxed environment," Russell said. "The coaches just let us go up there and do our thing."
That has worked so far for the Solar Sox, who entered Wednesday averaging 8.33 runs per game. Russell was one of four Mesa players with a hit and finished 1-for-3 with a walk. Brian Goodwin, the Nationals' No. 1 prospect, went 1-for-4 with a stolen base.
Peoria did a better job keeping the league's best offense in check. The Javelinas held the Solar Sox to three runs and four hits Wednesday, both season lows. Peoria starter Matt Heidenreich allowed one hit and struck out four batters in three innings.
Russell said Heidenreich did a good job mixing his pitches.
"He had some good offspeed stuff and kept us off balance the first three innings," Russell said.
Peoria scored its lone run in the first inning. Chris Taylor doubled off right-hander Tommy Collier to lead off the inning. He scored two batters later on a single from Japhet Amador. Collier then settled into the game and struck out three batters in three innings.
The Javelinas threatened in the bottom of the ninth against right-hander Lendy Castillo. Amador led off the inning with a double and Jorge Bonifacio, the Royals' No. 5 prospect, followed with a single. But Lendy got Aaron Altherr to ground into a double play and struck out Jonathan Meyer to close out the victory.
Taylor and Amador led the Javelinas offense. Taylor, the Mariners' No. 5 prospect, went 2-for-3 with a stolen base. Amador finished the game 2-for-4.
But it was the Solar Sox who put together a big inning and again walked off the field as winners. Russell said knowing Mesa can put together a rally at any time helps keep the team relaxed.
"We're stacked. Everyone in the Fall League has a stacked team," Russell said. "We're all getting pretty close and comfortable with each other. We're going to try to keep it rolling."