The Katusha rider, runner-up in Milan-San Remo last month, beat Dutchman Niki Terpstra in a two-man sprint after following the Etixx-Quick Step rider's attack 25 km from the finish of the 264.2km slog from Bruges.
Belgian Greg van Avermaet of BMC took third place ahead of Tinkoff-Saxo's Slovakian rider Peter Sagan.
Kristoff, 28, added the Tour of Flanders crown to the Milan-San Remo title he won last year -- his first win on one of the five 'Monument' one-day races.
"It was not easy, with Niki but I'm really happy, I had great legs today," said Olympic bronze medallist Kristoff who joined the Russian team in 2012.
Briton Geraint Thomas, who was among the top favourites, did not follow the decisive move and ended up outside of the top 10.
Terpstra attacked about 25 kilometres from the finish and Kristoff jumped into his wheel before the duo built a 30-second lead over a group of favourites.
Van Avermaet and Sagan also moved away in the final climb of the Paterberg, a brutal cobbled 400-metre climb at an average gradient of 12.5 per cent.
But they never came close to rejoining the leading duo.
After 23km of collaboration, Terpstram, knowing that Kristoff is a much faster sprinter, refused to take turns in front but the Norwegian, winner of the Three Days of La Panne warm-up race this week, did not panic.
He waited for Terpstra to make his move in the final straight and easily outsprinted the 2014 Paris-Roubaix champion.
One of the seven early breakaway riders, Jesse Sergent of New Zealand, crashed after being clipped by a neutral service car that was trying to ovetake the group in a curve.
His Trek team aid he suffered a broken collarbone that would require surgery.
Another neutral service car then crashed into the FDJ team car, which sent Sebastien Chavanel flying onto his back. FDJ said Chavanel was fine even if he went to a Gent hospital for further checks.
The classics specialists now turn their sights to next Sunday's Paris-Roubaix, labelled the "Queen of the classics".
(Writing by Julien Pretot; Editing by Martyn Herman)
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