Monday afternoon in downtown Tulsa, the former Clemson quarterback provided his second game-winning, walk-off hit.
Parker's one out home run in the bottom of the ninth inning broke a tie game and gave the Drillers a 3-2 win over Corpus Christi.
Friday night, the outfielder's ninth inning double gave Tulsa a 2-1 victory over San Antonio.
Three solo home runs accounted for all of Tulsas' runs in Monday's victory. All three came in the game's final three innings. The Drillers entered the game with only 7 homers in 12 games this season.
Parker said he was not necessarily trying to win the game with one swing of the bat. "I was just trying to hit something hard," he said. "He threw me one curveball that I swung through, but I saw it pretty well. Then he left one out and away and I was able to get a bat on it."
The first blast came courtesy of Henry Wrigley in the seventh inning and trimmed Corpus Christi's lead to 2-1. For Wrigley, it was the third straight game in which he has homered.
Angelys Nina tied the game in the eighth inning with a one-out homer, his first of the year.
The clutch hitting helped the Drillers overcome their struggles on the base paths. Nina's home run came two pitches after Rafael Ortega was thrown out trying to steal second base as the Hooks correctly guessed with a pitch out on the play.
During Parker's at-bat, pinch runner Delta Cleary Jr. was picked off first base after Kiel Roling drew a leadoff walk.
Tulsa's late rally overcame an early Corpus Christi lead as the Hooks scored single runs in each of the first two innings. The game's first batter, Austin Wates, drew a walk from Tulsa starter Dan Houston. He then stole second base before moving to third on a wild pitch. After Jiovanni Mier drew a walk, George Springer put the Hooks in front 1-0 with a line drive single into right field that scored Wates.
Corpus Christi doubled its lead with an unearned run in the second. With one out and the bases empty, Erik Castro reached on an error by Roling at first base. Castro moved to third on a double by Carlos Perez and scored on a base hit by Wates.
Parker's homer improved the Drillers record on their first homestand of the year to 4-1 with one game remaining. Their season record improved to 5-6.
"I'm just glad were winning," said Parker. "I'm just going up there trying to have a good at bat and a good approach and hope that something good happens."
Reliever Steven Hensley collected his first Drillers win. Hensley, who joined the team less than a week ago, pitched around a two out walk to work a scoreless top of the ninth.
Houston had his strongest outing of the season, surrendering five hits and two runs (one earned) in 5.2 innings.
Parker Frazier struck out four in 2.1 shutout innings in relief of Houston.
The Drillers will conclude their first homestand of the season Tuesday night at ONEOK Field. Christian Bergman (1-0, 0.79 ERA) will take the mound for Tulsa in the finale, while Corpus Christi will start Ruben Alaniz (0-0, 4.91). Starting time is scheduled for 7:05PM.
Fans that cannot make it to the game can still follow the action on live on AM1430 The Buzz in Tulsa. The broadcast will also be available on TulsaDrillers.com, or through the I Heart Radio app or website.