The Argentina international is considering a move to the Chinese Super League, with Shanghai Shenhua hopeful of signing him in a big-money deal, and has also suggested he could be set to retire.
But Tevez cemented his Boca legacy with a vital double as his side came from behind to win against their fierce Buenos Aires rival.
Both of last season's Primera Division derbies had finished 0-0, but there was much more drama this time around.
Visitor Boca had taken the lead through Walter Bou, but strikes from Sebastian Driussi and Lucas Alario put River in front at half-time.
Tevez came to the fore in the second half, levelling with a simple finish before scoring a magnificent curling effort with eight minutes remaining.
Ricardo Centurion then raced clear to seal the victory in the final minute as Boca continued its push for the title.