...that is, the Indians' two-run lead. The Twins left Nathan in their pen for 11 innings, including several with the game remaining tied 3-3. They later determined that after the Indians pushed across two runs and put men on second and third with no one out, now was the time to put him in to stop any further bleeding.
This is just awful. Yes, if you must win this game, it's crucial not to allow any further runs in this situation. To not allow any runs is also a very difficult job for any reliever, even one of the game's very best. More importantly, this is a far less critical situation than one which had come up many times earlier in this game: late innings, tie score.
Unless you're in a true must-win situation, there's little sense in using your best reliever if you are already going to lose the game the vast majority of the time. This is especially true when you have already refused to deploy your relief ace earlier in the game, when he could have made a real difference. This isn't even a save situation, so the Twins can't use that tired excuse. Not only did the Twins use inferior relievers in an important tie game, but now Nathan's availability is a concern for later in the series.
True to the non-results-oriented nature of this site, the Twins relievers left the game tied for several innings, and Nathan was ineffective, so maybe they would have lost this game even earlier had he been in. But had Ron Gardenhire done this, he would have made the right decision, and that's far more important in the long run.