Hill became the first pitcher since Pedro Martinez in 1995 to take a no-hit try into extra innings.
The Pirates didn't have a runner until Jordy Mercer led off the ninth with a sharp grounder that third baseman Logan Forsythe misplayed for an error. Hill retired the next three batters.
Hill (9-5) came back out for the 10th and Harrison sent his 99th pitch of the night into the first row of seats in left field, just out of the reach of Los Angeles leftfielder Curtis Granderson. Hill struck out 10 without a walk.
Juan Nicasio (2-5) picked up the win after working the top of the 10th.