Boston has been eliminated from first place.

To show that Boston is eliminated from first place, we start with the current standings:
            Team	W	L	GL	PCT	GB
        New York	94	68	0	0.580	0.0
       Baltimore	91	71	0	0.562	3.0
          Boston	81	81	0	0.500	13.0
       Tampa Bay	80	82	0	0.494	14.0
         Toronto	74	88	0	0.457	20.0
           Total	420	390	0

Boston can finish the season with at most 81 + 0 = 81 wins and will finish the season behind the following teams:
New York has already won 94 games.
Baltimore has already won 91 games.
# Boston Red Sox' magic number
# Boston's magic number
# Red Sox' magic number
# MLB Playoff Race