The Rangers prospect allowed one hit and three walks while striking out four over seven innings as the RoughRiders completed a three-game sweep of Corpus Christi with a 5-0 victory.
The win vaulted Frisco into the Texas League Championship Series for the first time since 2008.
Tepesch (1-0) retired the first 14 batters of the game and took a no-hitter into the sixth. Wilmer Font and Ross Wolf combined to get the last six outs, finishing off the RoughRiders' two-hitter.
"It was great. Every time I go out, I want to give the team a chance to win and, I mean, I did everything I could," Tepesch said. "The defense behind me made some great plays and I just decided to attack the hitters."
The 23-year-old right-hander began the year with Class A Advanced Myrtle Beach, going 5-3 with a 2.89 ERA over 71 1/3 innings before a promotion to the Texas League. He went 6-3 for Frisco with a 4.28 ERA, saving arguably his best start with the team for the most opportune time.
"If it's not the best [start of the season], it's right up there with a couple other ones I had," said Tepesch. "It was definitely added to it 'cause it was in the playoffs, to go out there, get the win, get us home for a day or so and get back out there and find out who we play in the championship."
The 2010 14th-round Draft pick made things a little easier for the RoughRiders in the series-clincher after they posted walk-off wins in each of the first two games.
On Wednesday, Chris McGuiness doubled home Leury Garcia in the ninth. One night later, Garcia homered in the ninth to give Frisco a commanding lead in the best-of-5 semifinal series.
In the clincher, McGuiness and Ryan Strausborger singled home runs in the sixth to provide Tepesch with all the support he needed. Guilder Rodriguez hit an RBI single in the ninth and Engel Beltre capped the scoring with a two-run double.
Tepesch, Font and Wolf took care of the rest.
"We were up, 2-0, and that was a goal of mine, to attack the hitters and do the best I could to get us out of here with a sweep, try to win this game," Tepesch said.
The RoughRiders will have three days to relax before the best-of-5 Championship Series begins.
"We walked off the first two games at our place, and that kind of gave us a lot of momentum," said Tepesch. "We have a great team and a good chance of winning this thing. We'll try to go into the next series and get off to a hot start [again] and see what happens."
In other Texas League action:
Springfield 4, Tulsa 2
Cardinals No. 2 prospect Oscar Taveras went 2-for-4 with a double, an RBI and a run scored as Springfield grabbed a 2-1 lead in the other semifinal series.
Catcher Audry Perez also had two hits, including a run-scoring double, for the Cards. Starter Kevin Siegrist earned the win after allowing two runs on four hits over five innings.
Kiel Roling slugged a solo homer for the Drillers. Gameday box score