The 23-year-old Russian took the biggest victory of his career as he beat Kris Boeckmans (Vacansoleil-DCM) and Adrien Petit (Cofidis) to the line in a bunch sprint after Geraint Thomas was caught inside the final 2km.
Team Sky were one of five World Tour teams in the 206 kilometres race and Welsh youngster Luke Rowe was in the break of the day.
The 22-year-old from Cardiff was part of a three-man escape that formed early in the race which took place on Walloon soil.
Along with Thomas Sprengers (Topsport Vlaanderen-Baloise) and Elias Van Breussegem of Continental team Doltcini Flanders, the trio built up a lead of 5:30 as the peloton crossed five short, steep climbs that came in quick succession.
Rowe left his fellow escapees as the riders completed five 16.5km laps which included the cobbled ascent of Côte de la Roquette.
But his advantage was under a minute as the former European junior track champion commenced the final lap and he was caught with 12km to go, denying him a chance of a second professional victory following his maiden success in the Tour of Britain last year.
But team-mates Thomas and Ian Stannard then hit the front, initially with Ignatas Konovalovas (MTN-Qhubeka) and Vacansoleil's Bert-Jan Lindeman before the Olympic pursuit champion went clear.
However he was caught inside the final 2km to set up the bunch gallop where second-year pro Tsatevich prevailed. Kenny de Haes and Alessandro Bazzana completed the top five.
Tsatevich said: "The team gave me a chance today, the whole race was done around me and I am thankful for that. I came to Belgium a little bit earlier than other members of Katusha, so I had some more days to train. That was one of the keys for today’s success.
"I was waiting for the massive sprint, but a rider from Europcar attacked before it. I took his wheel and was able to save the energy. In the last meters I started my sprint to win. I am happy to get first Russian victory for Katusha this year."
Dutch cyclist Ellen van Dijk of Team Specialized-Lululemon won the women's race.