Paxton (2-0) allowed one unearned run on four hits and a walk while striking out 10 batters over a career-high 7 1/3 innings in the Generals' 8-1 rout of the Mobile BayBears in Game 1 of the Southern League Finals.
"This is right up there. This was the biggest start of my professional career, for sure," Paxton said. "It's great to get this win for the team in the first game of the Championship Series.
"It was awesome to go out there and put the team on the right foot for the rest of the series. It was a great honor to start Game 1."
Tuesday's start marked the seventh time in his career -- and the second time this season -- that he recorded 10 or more strikeouts. It was also the fifth time this year that he pitched at least six innings and did not allow a earned run, and the seventh time in 23 starts where he walked one batter or fewer.
In two playoff starts, Seattle's No. 5 prospect has an 0.68 ERA with 19 strikeouts over 13 1/3 innings.
After allowing a leadoff bunt single to Evan Frey, Paxton retired the next 12 batters. Jonathan Griffin singled to left field to start the fifth, and Daniel Kaczrowski earned a free pass to begin the sixth, but neither hitter advanced into scoring position.
The only other Mobile batter to reach base against MLB.com's No. 81 prospect was David Nick, who singled to left to lead off the eighth, stole second base, advanced to third on a passed ball and scored on Kaczrowski's bloop behind second base.
"It was a fastball inside that I jammed the guy on," the 22-year-old said of Kaczrowski's RBI hit. "It just got over shortstop [Brad Miller's] head, it was just a little jam jar hit. But that's baseball, it happens. It was a good pitch, but he got lucky and popped it over the infield.
"My fastball was really good tonight and I was able to throw it to both sides of the plate. My curveball was good, and my changeup was the best it's been all season. I had been throwing it a little too hard velocity-wise, but I was able to slow it down and get some movement on it."
Paxton, who threw 79 of 115 pitches for strikes, was replaced by Mauricio Robles, who picked off Kaczrowski and fanned Frey to set down the side. In the ninth, Logan Bawcom worked around Matt Davidson's two-out single to seal the victory.
The outing was the second dominant performance of the postseason for Paxton, who struck out nine batters over six innings of three-hit ball in Game 1 of Jackson's 3-0 win over the Chattanooga Lookouts in the semifinals on Sept. 6.
"I feel like I struggled a little bit in the first half, but I've been better in the second half," said Paxton, who was selected in the fourth round of the 2010 Draft out of the University of Kentucky. "But it's getting better and better. My command has improved and my changeup is getting better. I'm getting really comfortable on the mound.
"It would be unreal [to win a championship]. It would be the biggest thing to happen in my professional career. I haven't won any championship since I was 13 years old. That was when I was back home playing Pee Wee Ladner baseball in a house league."
Paxton was 9-4 with a 3.05 ERA and 110 strikeouts over 106 1/3 innings this year. His nine victories ranked fourth in the Southern League, while his ERA would have been third on the circuit had he pitched enough innings to qualify.
Game 2 of the best-of-5 finals is in Jackson on Wednesday before the series moves to Mobile for the final three games.