The Mariners moved in front in the top of the ninth in a bid to win for just the third time in 12 games, but Tom Wilhelmsen was unable to hold the lead in the bottom half of the inning.
Venable came on as a pinch-runner after Yasmani Grandal had walked leading off the ninth, moved to second on Jedd Gyorko's single and took third on a passed ball.
A sacrifice fly to center by Kyle Banks brought home Venable to tie the game and Venable's single with none out in the 10th delivered Chris Denorfia from third to win it.
Luke Gregorson (3-2) claimed the victory by working the top of the 10th. Yoervis Medina (1-1) took the loss after failing to retire a batter.
San Diego starter Eric Stults did not figure in the decision following an eight-inning performance that included three hits and a dozen strikeouts.