With one out, Adam Jones reached on an error by third baseman Ty Wigginton, and Wieters brought him in with his third hit of the day.
The Orioles are now 9-2 on the year in extra innings with nine wins in a row, which is a new club record.
The Orioles improve to 34-26 and stay within a game of first-place Tampa Bay, who also won this afternoon. The Orioles have now won two series in a row after losing four straight.
Jason Hammel started today for the Orioles and struggled badly with his control, issuing a season-high five walks, along with a run-scoring wild pitch, over six innings. He gave up six hits and four runs, throwing 115 pitches.
Philly's Cliff Lee was looking for his first win of the year in his tenth start, but didn't get it because he could not protect a 4-1 lead. Down by three in the last of the fourth, Mark Reynolds walked and Steve Pearce doubled with two outs.
Then, Steve Tolleson drove one down the left-field line for a game-tying three-run homer. His second homer of the season came on a 1-2 pitch and tied the game, 4-4.