After a wild pitch that advanced Jarren Duran from second to third with no outs, and a strikeout from Ceddanne Rafaela and a walk from Marcelo Mayer, Yoshida, 32, hit a bouncing single over the infielders into right field to win the game.
Yoshida now brings his season batting average to .310 and OPS to an .888 as the Red Sox improved to 8-11.
Detroit had multiple chances to get on the board.
In the top of the ninth inning, they had runners on second and third with two outs. But Red Sox reliever Aroldis Chapman got out of the jam.
Then, once more in the 10th, the Tigers had a Dillon Dingler on third with one out, but couldn't bring him in as reliever Garrett Whitlock got out of it.
Both teams had four hits each, with Jahmai Jones having two of those for the Tigers, who fell to 10-10.