Berg was 7-1 with a 0.73 earned-run average with 12 saves this season. He is UCLA's all-time leader in saves with 48.
Savage, in his 10th season, led the Bruins to the Pac-12 championship with a 22-8 conference record, a school record for victories. It was UCLA's third conference since 2011.
UCLA's Grant Dyer, Ty Moore, Kevin Kramer, James Kaprielian and Grant Watson were also named to the first team.
Stubbs, a catcher, threw out 54% of base stealers while hitting .330 this season.