In that particular situation, Wedge owed it to starter Cliff Lee to allow him to finish the game. Lee, the reigning American League Cy Young Award winner, had the game under control. He was leading 5-2, and was cruising to a much-needed win for himself and a desperately-needed win for the Indians.
Lee had only thrown 101 pitches. That's fewer pitches than he has thrown in any of his starts this season, with the exception of opening day. Lee also had an extra day's rest since his previous start. Put it all together _ a starter who is dominating the opposing team, a relatively low pitch count, and a pitcher working with an extra day's rest _ and there was no reason for Lee to be taken out of the game after the eighth inning, unless Lee said he was tired.
Another factor is Lee is the Indians' No.1 starter. The No.1 starter has earned the right to, within reason, finish any game in which he's in position to. Wedge owed it to Lee to allow him to finish that game. The Indians, moreover, had lost three games in a row prior to Tuesday. They had their ace, Lee, matched up against Kansas City's No.3 or 4 starter, Brian Bannister. Wedge also knows the Indians will be facing Zack Greinke - the best pitcher in the league thus far - in the final game of the series. That made winning the first game with his ace on the mound, an even bigger priority for Wedge.
The Indians were in a position to win Tuesday's game. Their ace was cruising, his pitch count was down, he was working with an extra day's rest. There was no reason not to allow him to finish. Had any of the Indians other starters been in that situation, it would have been justified to bring in the closer. But not with Lee. Not there. Not after Lee had been denied so many wins this season due to a lack of run support, and was, on Tuesday, in position to close out his own victory.
But instead Wedge removed Lee from the game, brought in closer Kerry Wood, and a few minutes later the Indians had lost four in a row.