Braces by Georgian midfielder Zhano Ananidze and Dutch forward Quincy Promes gave nine-time champions Spartak an impressive victory.
“It’s nice to start the new season with a win,” Spartak manager Dmitry Alenichev said.
“I set my players a task to score an early opener and they achieved that. It helped us a great deal, while our third goal decided the game.”
Spartak started brightly and in the sixth minute Promes found Ananidze unmarked in the area, and the 23-year-old had enough time and space to find the net with an angled shot.
Arsenal poured forward seeking an equaliser but squandered their few chances.
Ananidze had the Spartak fans on their feet in the 34th minute when he grabbed his second of the match with a 30-yard screamer.
Two minutes after the interval, Promes made it three by turning in Dmitry Kombarov’s cross from close range.
Promes rounded off the scoring in the second minute of injury time with a shot from just inside the area.
In Sunday’s early encounter, Ural Yekaterinburg also started the season with a confident 2-0 win over Ufa.
Midfielder Roman Emelyanov put hosts Ural ahead in the fifth minute with a powerful shot from the edge of the box, and former Tottenham Hotspur striker Roman Pavlyuchenko added the second just before half-time.
“It was a good match and I’m especially pleased that we kept a clean sheet today as we’ve done a lot of work to improve our defensive play,” Ural head coach Vadim Skripchenko said.
“I’d say we won deservedly.”
Elsewhere, Terek Grozny also chalked up a win, beating Samara 1-0.
Romanian midfielder Gheorghe Grozav scored the only goal in the 75th minute with a Panenka-style penalty after Albanian Odise Roshi was foule