The 25-year-old struck in either half to make it a hat-trick of successive gold medals for coach Markus Weise, who also coached Germany's women to victory in 2004 and was in charge of the men at Beijing 2008.
Prior to the final, Rabente had scored only six times in 77 internationals, and the only player in the squad with fewer goals was goalkeeper Max Weinhold.
However, he produced a brilliant first just before half-time and, after penalty corner specialist Mink van der Weerden had equalised after the break, he deflected in a second five minutes from the end.
Earlier in the day, Australia claimed the bronze medal with a 3-1 win over Host Nation Great Britain.
Weise said: 'It was a super final full of good Hockey and fighting spirit from both sides - two top teams. A final always has one sweet part and one bitter part, today we got the sweet part of it.'
Player Max Mueller said 'It's unbelievable. After the hard pool matches, we never thought about it. We just thought about the next match and getting better in the tournament. Getting this medal is unbelievable.'
Floris Evers, of the Netherlands, said: 'I was really proud of the inexperienced players - I told them after the game that they need to do it in Rio. They really deserve a gold medal, but for now, compliments to the Germans that they did it again in the final.
'I think it was a 50-50 game. Maybe if Rabente did not make it 2-1, I would have scored one myself. I think we didn't play the best play we could, maybe because it was a final, that is the only disappointment I have.
'I'm proud of the silver medal, it is my second. They call me 'silver medallist' - that's a shit name. I wanted to change that here, but it's still an Olympic medal.'