[bbstpkiv] Deviously eliminating a rival

Eliminating a rival by losing.

In the Red Sox-Yankees rivalry, pretend it's late in the season and the Red Sox have already unfortunately been mathematically eliminated from the playoffs, while the Yankees are in a playoff race against, say, the Orioles. The Orioles are doing a little better, on the verge of clinching (and thus eliminating the Yankees) if they win today's game.  Today's game is against the Red Sox.  The Red Sox lose the game (perhaps amid difficult-to-prove allegations of throwing the game) to cause the elimination of their hated rival. 

This could also happen if the Red Sox have already clinched a playoff berth and home field advantage, while the Yankees and some other team are in a race for the wildcard spot.

How many times in baseball, or other sports, has a team eliminated a rival this way, or been in a position to do so?

The enemy of my enemy is my friend.