The Mariners' No. 5 prospect struck out nine and allowed three hits over six innings as Jackson blanked Chattanooga, 3-0, in Game 1 of the Southern League semifinals.
Paxton faced five over the minimum while throwing 58 of his 88 pitches for strikes. He walked two and allowed just two runners to advance to second base.
"I just wanted to go in there and force contact and throw strikes and make those guys earn everything that they got," Paxton said. "The strikeout pitch was the fastball and the curveball, at times, was real good and they couldn't hit it."
Paxton likely would have continued to pitch deeper into the game had it not been for a rain delay that lasted more than two hours.
"It was too bad, I was feeling good," the 23-year-old left-hander said, "My pitch count wasn't too high and I think I would've gone another inning or two."
Paxton saw his season take a turn for the better in the second half, going 6-1 with a 2.40 ERA in 11 starts for the Generals, more than a run better than his first-half ERA. The Canadian native felt that the difference was being able to mix up his pitches.
"The biggest key for me is getting ahead of hitters," he said. "I get in trouble when I get behind in counts and guys can cheat on fastball. Getting ahead and making them respect my other pitches is big for me."
Catcher Mike Zunino, the club's No. 4 prospect and first-round selection in June, put the Generals on the board with a third-inning RBI double.
"He's great," Paxton said of his batterymate. "He catches the ball really well, he calls a good game, and obviously, he's a great hitter at the top of the lineup. It's a plus to have him on the team."
Yoervis Medina allowed a hit over two innings of relief and Logan Bawcom tossed a hitless ninth to earn the save for the Generals.
Matt McGill, the Dodgers' No. 8 prospect, took the loss after allowing a run on seven hits while fanning five over six innings for the Lookouts.
In other Southern League playoff action:
Mobile 5, Montgomery 3
Chase Anderson struck out nine and allowed two runs on eight hits over five innings as the BayBears took the opening game of their best-of-5 semifinal series. D-backs' No. 5 prospect Chris Owings plated a pair of runs and David Nick was 3-for-3 with two runs scored for Mobile. Mikie Mahtook, the Rays' No. 4 prospect had three hits and two RBIs in the loss for the Biscuits. Gameday box score