UNC (54-13) has won nine in a row since its early exit in the ACC Tournament.
After the game, teammates chided him for his lack of speed, but it was Flack's wheels that enabled him to reach third on a leadoff hit to the right field corner.
"He's deceptively fast," joked Miller. "We were all waiting for him to run out of gas when he came around second."
Then, two pitches later, Flack raced home with the eventural game-winning run when the ball got by OSU catcher Mitch Canham.
When asked how the ball got away, a dejected Canham simply responded, "You saw it; it got past. They scored; they win."
After the Tar Heels jumped out to a 2-0 lead in the first inning on RBI singles by Jay Cox and Tim Federowicz, the Beavers (48-16) answered with a run in the third and took the lead on a two-run homer by Cole Gillespie.
Then lightning struck in the distance, followed by a downpour which delayed the game for over an hour.
Miller (5.0 IP, 7 H, 3 ER, 1 BB, 5 K) was done, in favor of reliever Jonathan Hovis. But OSU starter Dallas Buck remained in the game.
The difference in coaching maneuvers proved crucial, as Hovis allowed just one hit in 1.2 innings; while Buck, who gave up nine hits on the night, allowed an earned run in the sixth that enabled Carolina to tie the score at 3 apiece.
"I have a lot of confidence in our bullpen," UNC coach Mike Fox said. "Andrew was out there for 70 minutes and I didn't feel too good about putting him back out there. He has a great future ahead of him and I didn't want to jeopardize that in any way."
After Flack's heroics, Hovis came out for the ninth but immediately walked Chris Kunda, who would advance to second on a sacrifice bunt by Canham. So Fox went to right-handed fireballer Andrew Carnigan, who struck out the remaining two Beavers and picked up his 15th save of the season to secure the victory.
Meanwhile, Hovis (8-2) got the win, while Joe Paterson (1-1) was credited with the loss.
"This puts us in a good position to come out and win a national championship," Flack said.
The two teams square off for Game Two on Sunday at 7 p.m. The game can be seen on ESPN2.
With one more victory, Carolina would become the first ACC team to take home the CWS title in 51 years and only the second all-time. Wake Forest won it all in 1955.