The 27-year-old Norwegian, who came of age last year by winning Milano-Sanremo and two stages of the Tour de France, powered clear of Nacer Bouhanni (Cofidis) and Bryan Coquard (Europcar) to win the 196.5km stage from Saint-RÃ©my-lÃ¨s-Chevreuse to Contres.
There was no change to the top three on the overall standings; following Monday's prologue in Maurepas, overnight leader Michal Kwiatkowski (Etixx-Quick-Step) remains tied on the same time as Rohan Dennis (BMC Racing), with Kwiatkowski's teammate Tony Martin seven seconds back in third place.
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Etixx-Quick-Step was not all smiles, however, with Tom Boonen a notable DNF on Stage 1.
17 kilometres from the finish, the four-time Paris-Roubaix champ and three-time winner of the Tour of Flanders touched wheels with the rider in front of him and came crashing down, immediately clutching his left collarbone, and was no sooner announced as an abandon.
The day's protagonists, Anthony Delaplace (Bretagne-SÃ©chÃ© Environnement) and Thomas Voeckler (Europcar), escaped some 40 kilometres into the stage, and at one point amassed a lead of just over six minutes.
Despite their advantage being whittled to under a minute with 33km to go, a poorly structured chase saw their lead back out to two minutes, before a concerted effort by Team Sky and Lotto-Soudal reeled the duo back in just a kilometre from the line.
The race continues with a 172-kilometer stage from the ZooParc de Beauval zoological park to Saint-Amand-Montrond in central France.
Stage 1: 196.5km, Saint-RÃ©my-lÃ¨s-Chevreuse - Contres
1 Alexander Kristoff (NOR) Team Katusha 5:15:18
2 Nacer Bouhanni (FRA) Cofidis, Solutions Credits
3 Bryan Coquard (FRA) Team Europcar
4 Heinrich Haussler (AUS) IAM Cycling
5 Giacomo Nizzolo (ITA) Trek Factory Racing
6 Jose Joaquin Rojas (ESP) Movistar Team
7 Moreno Hofland (NED) Team LottoNL-Jumbo
8 Niccolo Bonifazio (ITA) Lampre-Merida
9 Ben Swift (GBR) Team Sky
10 Michael Matthews (AUS) Orica GreenEdge
1 Michal Kwiatkowski (POL) Etixx - Quick-Step 5:22:58
2 Rohan Dennis (AUS) BMC Racing Team
3 Tony Martin (GER) Etixx - Quick-Step 0:00:07
4 John Degenkolb (GER) Team Giant-Alpecin 0:00:09
5 Luis Leon Sanchez (ESP) Astana Pro Team 0:00:10
6 Lars Boom (NED) Astana Pro Team
7 Michael Matthews (AUS) Orica GreenEdge
8 Sylvain Chavanel (FRA) IAM Cycling
9 Tom Dumoulin (NED) Team Giant-Alpecin 0:00:13
10 Geraint Thomas (GBR) Team Sky