Heyward opened the scoring with a two-run homer in the fifth, scored the go-ahead run in the seventh after Arkansas tied it and delivered again after Willie Abreu doubled off the center-field wall to open the Miami ninth.
Heyward rounded first base and tossed his helmet high in the air as pinch runner Carl Chester scored.
The Hurricanes (50-16) move to a Wednesday game against Virginia or Florida. The Razorbacks (40-25) went two-and-out at the CWS for only the second time in eight appearances.
Bryan Garcia (6-2) earned the win after getting out of a bases-loaded situation in the top of the ninth. Zach Jackson (5-1) took the loss.
Heyward, the Hurricanes' No. 9 batter and the younger brother of St. Louis Cardinals outfielder Jason Heyward, has reached base in six of eight plate appearances in two games.
He drilled a Jackson Lowery pitch into the left-center seats in the fifth inning for the first CWS home run between the power alleys in the five years the event has been held at the spacious TD Ameritrade Park. It was Heyward's fourth of the season.
After the Hogs tied it 2-2 in the seventh, Heyward singled in the bottom half and stole second. He went home when shortstop Michael Bernal threw wildly to third trying to get him on a groundball. The ball bounced into the screen in front of Miami's dugout, and Heyward scored ahead of Lance Phillips' throw to the plate.
The Hogs tied it in the eighth on a nice piece of hitting by Brett McAfee. McAfee initially showed bunt with runners on first and second, prompting second baseman George Iskenderian to shade to his left in case he needed to cover first. McAfee pulled back and slapped a soft bouncer through the hole, allowing Tyler Spoon to score.
Arkansas loaded the bases in the ninth, but Garcia got Rick Nomura to ground out to end the inning.
Virginia 1, Florida 0: The Cavaliers' Brandon Waddell gave up two hits over seven-plus innings and got shutdown relief help from Josh Sborz in a victory over the Gators.
Virginia (41-22), the 2014 national runner-up, took control of its bracket and is off until Friday. The Cavaliers need one more win to reach next week's best-of-three finals.
Florida (50-17) will play an elimination game Wednesday against Miami, the team the Gators beat by 12 runs in their Omaha opener.