Liechtenstein almost found an unlikely equaliser on the quarter-hour mark when Sandro Wieser's long-range free kick grazed the left-hand post.
Russia, who were European semi-finalists in 2008, doubled their lead courtesy of another own goal five minutes after the interval.
Alan Dzagoev ran clear on goal and even though his shot was saved by Jehle, the ball bobbled up and was inadvertently turned home by Mario Frick.
Soon after it was three when Frick upended substitute Artem Dzyuba in the box, with Dmitir Kombarov making no mistake from 12 yards.
Dzyuba then got himself on the scoresheet and it was a first international goal for the Spartak Moscow man as he slotted home Kokorin's cutback.
The other four teams in Group G meet later tonight, with Sweden travelling to Austria and Montenegro hosting Moldova.