Joseph drove in three runs as Philadelphia, a major league-worst 23-48, won for just the second time in 15 games.
Nola (4-5) allowed one run, four hits and two walks in 7 1/3 innings and struck out eight.
Paul DeJong homered on a hanging curveball leading off the eighth, pulling the Cardinals to 3-1, and Matt Carpenter walked with one out. Pat Neshek relieved and got Tommy Pham to ground into an inning-ending double play, and Luis Garcia followed with a perfect ninth.
