Tampa Bay had first choice because of a 16-10 record against the Red Sox and Angels this year, while Boston had second pick for going 12-14 in head-to-head games. Los Angeles was 6-10.
In the event of a three-way tie, the Red Sox would host the Angels on Thursday, with the winner hosting the Rays on Friday.
For a two-team tie, the Rays would host the Red Sox because Tampa Bay won the season series 12-6.
Boston began Monday one game ahead of Tampa Bay and two games in front of Los Angeles.
In the NL, St. Louis would host Atlanta in a tiebreaker on Thursday because the Cardinals won the season series 5-1. The Braves entered Monday with a one-game lead.