Barnett earned the save in Thursday's 9-6 win over the Giants, striking out one in a perfect ninth inning.
It's Barnett's second save in his first eight appearances in the majors this season. The 25-year-old right-hander has quickly ingratiated himself in the A's bullpen, allowing just two runs on seven hits and seven walks while striking out 19 in his first 14.2 innings. Barnett made five starts with Triple-A Las Vegas earlier in the year, where he posted a 4.64 ERA over 42.2 innings, but he's now pushing for a high-leverage role in the majors.