Facundo Roncaglia (35) gave Boca the lead in the 17th minute but Johan Carbonero (23) equalised within three minutes, with the score remaining at 1-1 until deep into stoppage time.
Piovi turned hero for Racing in the dying minutes of the final, played outside Argentina for the first time, as he scored from the spot to claim the trophy, two months after they won the Champions Cup.
Boca Juniors had gone ahead after Roncaglia fired a powerful volley in at the near post, but Carbonero equalised soon after by latching onto a pinpoint through ball from Maxi Moralez before unleashing an incredible shot from distance.
Both Boca Juniors and Racing came close in the second half but late drama decided the contest as Racing were awarded a penalty for a handball incident by Agustin Sandez.
Piovi smashed in his spot-kick to wrap up the match.