They narrowly missed out on gold just 0.43secs after Slovakia who finished in a time of 101.58. France took Bronze with 103.24.
In the semi-final earlier in the day the pair made a good start, but suffered a couple of penalties and looked potentially in trouble at gate 19.
German canoe coach Henze dies from car-crash injuries
And it was trouble at the same place on the course in the final that lost them a marginal lead over the eventual victors.
There was further drama in the final as the Czech Republic's Jonas Kaspar and Marek Sindler - who finished second in their earlier semi-final - capsized, costing them a medal.
David Florence and Richard Hounslow claim silver in the C2 event
Image credit: Reuters
The result repeats the British pair's success in the London 2012 games.
Hoping to add to Great Britain's canoe haul, with Joe Clark taking a gold medal in the previous night's action, was Fiona Pennie in the women's C1 final.
But it wasn't to be, despite finishing second in the earlier semi-final, after incurring some penalties she was some seven seconds off the top spot and Spain's Maialen Chourraut took gold with a time of 98.65.
German coach suffers life-threatening injuries in taxi crash
Britain's Joe Clarke strikes gold in K1 slalom canoeing