It was the second goal of the game for Rabente and it came just 9 seconds after goalkeeper Jaap Stockmann made a save that kept the contest tied.
Germany had lost to the Netherlands during the round-robin portion of the tournament, but prevailed when it mattered most to win their second straight Olympic gold medal.
Germany also won the title at the 1992 Olympics.
Mink van der Weerden scored in the 54th minute to tie it for the Netherlands, which was trying to join the women from that country in winning this year's Olympic crown.
It was the fourth medal in the last five Olympics for the Netherlands, which won gold in 1996 and 2000.
Australia won the bronze medal with a 3-1 victory over Britain in the third-place match. These were the sixth straight Olympics in which Australia had won a field hockey medal.