Ari struck either side of the interval and compatriot Ibson added a third goal one minute from time for the Russians.
Spartak, holders of the unenviable record of 22 successive Champions League matches without a win, have now won two out of two and top the group on six points after beating Olympique Marseille 1-0 two weeks ago.
"We played almost an ideal match tonight," a beaming Spartak coach Valery Karpin told a news conference. "I couldn't have asked for anything more from my players."
The Slovak side rarely threatened Spartak keeper Andriy Dykan on the wet, artificial Luzhniki turf as they slumped to their second consecutive defeat after being thoroughly outplayed by Chelsea 4-1 in their opener.
With rain falling on the Russian capital for most of the day, making the synthetic pitch slippery, both teams were resigned to making long-range shots on goal.
LOOPING HEADER
The home team increased the pressure midway through the first half and it paid off when Ari sent a looping header beyond the reach of advancing Zilina keeper Martin Dubravka.
The ball clearly crossed the goal-line in mid-air before being cleared by a Slovakian defender.
Swedish referee Martin Hansson hesitated for a few seconds before awarding the goal after getting help from one of his assistants positioned in the penalty area.
Ari doubled his tally just after the hour, tapping in a Dmitry Kombarov cross. Ibson sealed a comfortable victory for the hosts, redirecting another cross from the left wing by fellow substitute Christian Maidana with time running out.
The only negative aspect for the Russians was the injury to their top striker, Brazilian Welliton, who limped off the pitch with an apparent hamstring pull midway through the second half.
Spartak's real test of their Champions League credentials should come in three weeks when they face the seemingly unstoppable Chelsea, who were hosting Marseille in the other Group F match later on Tuesday.
A win over the English champions would almost ensure that Spartak reached the knockout round for the first time since the 1995-96 season.
