The Norwegian powerhouse won the sprint from a reduced peloton to take his 11th victory of the season after a crash in the finale had brought down a number of riders, and held up even more.
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Edward Theuns (Topsport Vlaanderen) took second place, with Belarusian Yauheni Hutarovich (Bretagne Seche Environnement) in third.
Seven riders formed the day’s escape group after around 30 kilometres of the 200km route from Antwerp to Schoten: Frederik Backaert (Wanty-Groupe Gobert), Matteo Busato (Southeast), Laurens De Vreese (Astana), Huub Duyn (Roompot), Vincent Jerome (Europcar), Tanner Putt (UnitedHelathcare) and Kenneth Van Bilsen (Cofidis).
The break was tightly controlled by a combination of teams at the front of the peloton, and achieved its biggest gap over the bunch of four and a half minutes at the 50km point.
After that, the gap was slowly but surely chipped away. With 25km to go, it was just 23 seconds as Katusha led the chase, but the break was allowed to dangle out the front until the final 4km when the catch was made.
Etixx-QuickStep moved into the driving seat, with Sky and Katusha just behind them. Disaster struck in the final kilometre, as a crash near the front of the peloton brought down a swathe of riders. A handful were left to contest the sprint, but none could match the in-form Kristoff.
Defending champion Marcel Kittel (Giant-Alpecin) elected not to start the race after a lingering illness that started at the Tour Down Under in January. Also absent was three-time winner Mark Cavendish (Etixx-QuickStep) and fellow sprinter Andre Greipel (Lotto-Soudal).
Scheldeprijs 2015: Antwerp to Schoten, 200km
1. Alexander Kristoff (Nor) Katusha
2. Edward Theuns (Bel) Topsport Vlaanderen
3. Yauheni Hutarovich (Blr) Bretagne Seche Environnement
4. Marc Sarreau (Fra) FDJ
5. Danny Van Poppel (Ned) Trek Factory Racing
6. Matteo Trentin (Ita) Etixx-QuickStep
7. Nicolas Marini (Ita) Nippo-Vini Fantini
8. Michael Van Staeyen (Bel) Cofidis
9. Tyler Farrar (USA) MTN-Qhubeka
10. Christoph Pfingsten (Ger) Bora-Argon 18 all same time