Minnesota has been eliminated from first place.

To show that Minnesota is eliminated from first place, we start with the current standings:
            Team	W	L	GL	PCT	GB
       Cleveland	85	77	0	0.525	0.0
 ChicagoWhiteSox	84	78	0	0.519	1.0
       Minnesota	77	85	0	0.475	8.0
         Detroit	76	86	0	0.469	9.0
      KansasCity	69	93	0	0.426	16.0
           Total	391	419	0

Minnesota can finish the season with at most 77 + 0 = 77 wins and will finish the season behind the following teams:
Cleveland has already won 85 games.
ChicagoWhiteSox has already won 84 games.
# Minnesota Twins' magic number
# Minnesota's magic number
# Twins' magic number
# MLB Playoff Race