Baxter, a senior righthander, allowed four hits with one walk and eight strikeouts. He faced just 24 batters in a baseball game shortened to six innings because of the 10-run mercy rule.
"I'm having fun out there," Baxter said. "I'm just trying to throw strikes, and the guys have been making the plays behind me."
Baxter (6-1) has thrown 30 consecutive scoreless innings. He last allowed a run in the fourth inning of an 11-1 victory over Bishop Eustace on April 21.
"He's a senior," St. Augustine coach Mike Bylone said. "He's been pitching since his freshman year, but he waited his turn behind some other guys. That's how our program is built."
Baxter, who lives in Waterford and plans to play baseball next season at Rowan University, also delivered the game's biggest hit: a three-run double that gave the Hermits a 5-0 lead in the fifth inning.
"I needed that because I've been struggling at the plate," Baxter said.
Mike Elfreth and Kyle Lindsay had two-run singles and Mike Scimeca had a pair of doubles and scored two runs - all in an eight-run sixth inning for St. Augustine (12-6), which has won six of seven.
St. Augustine, which made the Diamond Classic final last season, advanced to face Washington Township in next Saturday's quarterfinals. Washington Township advanced with a 7-3 win over Eastern in the first game of the doubleheader at Deptford.
Baxter faced six batters with runners in scoring position. He struck out four of them.
"The first five innings, he had great command of his curveball," said St. Augustine catcher Barry Buchowski, who was 2 for 3 and reached base three times.
Baxter was the losing pitcher in last year's Diamond Classic final, won by Buena by a 9-8 score in a game that ended with a bang-bang play at the plate.
"I want that one back," Baxter said. "That's my goal, to get back there and win it this time."
St. Augustine 010048 - 13141
Sacred Heart 000000 - 044
WP: Kevin Baxter. LP: Holvin Figueroa. 2B: SA-Mike Scimeca 2, Christian Adorno, Kevin Baxter; SH-Steve Steigerwalt.
Contact Phil Anastasia at 856-779-3223, firstname.lastname@example.org, or @PhilAnastasia on Twitter. Read his blog, "Jersey Side Sports," at www.philly.com/jerseysidesports