The Athletics completed a three-game sweep, holding the Yankees without a run for 17 innings after Robinson Cano hit a two-run homer in the first.
The teams then slogged their way through a long series of missed opportunities in a game that saw 14 pitchers take the mound. The teams combined to strand 26 runners and Oakland boosted its record to 21-5 since May 17.
Jaso reached on a single off rookie Preston Claiborne (0-1) with one away in the 18th and the Yankees then brought in Mariano Rivera to try to get out of the inning.
Smith, however, moved Jaso to third with a base hit and Jed Lowrie was walked intentionally to load the bases. Freiman then singled on a 1-0 pitch to end the contest -- one that took 5 hours, 35 minutes to complete.
The Athletics turned the game over to reliever Jesse Chavez (1-0) in the 13th inning and he struck out seven over 5 2/3 to get the win.