MLB tie-breakers

My brain hurts! I'm still trying to find out how the Yankees clinched first place today? They are 1 game up on the Red Sox with one game to go... against Boston. One would think that if the Red Sox won that game, the two teams would be tied and then a tie-breaker game would be played on Monday.

I definitely heard someone on the news say that the Red Sox had to win 2 of 3 in the final series to force the 1 game playoff on Monday vs the Yankees.

If someone can post an explanation of the rule (in English!) please do so before I injure my brain trying to work it out.