Farrell sank two foul shots with 18.1 seconds left to seal the victory also dished off four assists for the Hoosiers (12-5, 2-2 Big Ten), who bounced back from a 10-point, second-half deficit to break a 12-game skid against Wisconsin.
After Sam Dekker hit a 3-pointer to give Wisconsin a 52-42 lead with 13:30 remaining, Indiana went on a 19-5 run to grab the lead for good.
Stanford Robinson provided 13 points off the bench and Will Sheehey aded 13 with six rebounds.
Traevon Jackson netted 21 points for Wisconsin (16-1, 3-1 Big Ten), which saw its school-record winning streak snapped.
The loss left Arizona, Syracuse and Wichita State as the lone unbeaten teams in the country.