The Quick Step Floors rider powered away from the group of favourites 28km from the finish line.
Smeared with dust on his face, he whizzed past three breakaway riders on the intimidating Oude Kwaremont, a 2.2-km cobbled climb at an average gradient of 4.2 percent, and never looked back.
Denmark's Mads Pedersen took second place ahead of last year's winner Philippe Gilbert of Belgium, one of Terpstra's team mates.
A couple of hours after Olympic champion Anna van der Breggen of the Netherlands won the women's race after a solo breakaway, Terpstra used his tactical nous and his team's strength to snatch an emphatic win after victories in Le Samyn and the GP E3-Harelbeke.
Dylan van Baarle (Team Sky), Sebastian Langeveld (EF Education First-Drapac) and Pedersen (Trek-Segafredo) attacked with about 40 kilometres left but were caught by Terpstra at a key point of the race.
After a cobbled sector, Vincenzo Nibali sped away from the group of favourites but Terpstra jumped onto his wheel.
He was, however, too powerful and went solo, bridging the gap to the leading trio at the foot of the Oude Kwaremont.
Terpstra was clearly the strongest and extended his lead in the final uphill cobbled sector, the Paterberg, and held off Pedersen and the group of favourites.
The Tour of Flanders is the second of the five 'Monument' one-day races after Milan-San Remo and ahead of next weekend's Paris-Roubaix, the Liege-Bastogne-Liege and the Tour of Lombardy.
(Writing by Julien Pretot; Editing by Toby Davis)
