Anisimov broke the deadlock 5:45 into the second with a backhander off a pass from Tim Erixon. Fedotenko doubled the lead on a power play less than three minutes later. Erixon and Michael Del Zotto assisted on the second goal.
Sparta wasted several chances in the first period before the Rangers took charge in the second.
The Rangers resume their European tour against Frolunda in Sweden on Friday, Slovan Bratislava in Slovakia on Sunday and EV Zug in Switzerland on Monday.