Reynolds reached on a one-out single in the 10th and advanced to second on a single by Brian Anderson. Reynolds scored when Bulldogs catcher Kyle Arnsberg sailed a throw into the outfield trying to catch Reynolds stealing third.
"I told Reynolds if you feel you can steal, make sure you get a good jump and keep your eyes out," Arkansas coach Dave Van Horn said. "He didn't go on the first pitch and went on the second, which was a breaking ball, which was perfect. I didn't think the catcher was going to throw because there was no way he was going to throw him out.
The Razorbacks (36-17) improved to 3-0 all-time in North Little Rock's minor league ballpark, beating Louisiana Tech in 10 innings for the second time in three years. A record crowd of 10,512 packed the stadium for the Hogs' annual trip to central Arkansas.
They weren't happy early as Louisiana Tech roughed up Arkansas starter Trent Daniel for two runs in the top of the first inning, but the Razorbacks responded with three in the bottom half to take a 3-2 lead.
Reynolds' two-run double tied the game and he later scored from second on a Bo Bigham infield single.
Playing their first game in 10 days, the Bulldogs (23-24) regained the lead in the top of the third on Bre'shon Kimbell's two-run ground rule double, which came in the first pitch from Razorbacks reliever Nolan Sanburn.
Sanburn, who struggled in a start last Saturday against Auburn, settled down after the hit, allowing no earned runs in 3 1/3 innings and striking out five.
"It might have been the best he'd thrown all year," Van Horn said. "He kept a couple of balls up, but for the most part when he missed, he missed down and away. His velocity looked good and he was throwing it more where he wanted to, and that was a positive."
Reynolds tied the game with a solo home run to lead off the bottom of the fifth inning - his sixth this season. The junior finished the game a triple shy of the cycle and upped his batting average to a team-leading .350.
"I felt comfortable and confident," Reynolds said. "I've felt like that the last couple of weeks and hopefully it carries over to Tennessee.
"We've lost a lot of one-run games. It feels good just to get a win, no matter what kind of win it was."
Arkansas took the lead on Dominic Ficociello's sacrifice fly to score Matt Vinson in the sixth, but the Bulldogs tied the game 5-5 on a RBI double from Taylor Terrasas in the top of the seventh.
The Razorbacks loaded failed to score for the third time with the bases loaded in the eighth and a base-running error from Jimmy Bosco allowed the Bulldogs to turn a double play and get out of the ninth.
Arkansas stranded 15 runners Tuesday.
"We left a lot of runners out there," Van Horn said. "The good thing is we got the runners on. We did a good job of making them throw strikes and spraying the ball around the field.
"We could have broke it open early. Hopefully that will happen this weekend, to get those hits."
Ryan Gebhardt led off the top of the 10th with a walk for Louisiana Tech, but Barrett Astin struck out the next three batters to strand him at second base and set up the heroics in the bottom of the inning.
Astin picked up the win for Arkansas, pitching two scoreless innings and allowing just one walk. The Razorbacks' bullpen, which was roughed up in consecutive home weekend losses to South Carolina and Auburn, recorded 7 1/3 scoreless innings.
"(Pitching coach Dave Jorn) sat us down after the last Auburn game and we had a little come to Jesus meeting, and figured some things out," Astin said. "We figured some things out and tried to get back to where we were in the beginning of the season."
Caleb Dudley, one of eight Louisiana Tech pitchers used Tuesday, was assessed the loss.
The Razorbacks will close out the regular season with a three-game series at Tennessee, beginning Thursday.