The Swede birdied the first playoff hole with a gutsy long putt to wrap up the victory.
Lundberg, who made three birdies in a row on his way to a 65, and Wiesberger, who shot 69, were tied at 12 under after the fourth round.
Defending champion Joost Luiten, who teed off the final day with a two-stroke lead over Wiesberger, carded a par 72. The Dutchman finished third, one stroke off the lead.
England's Lee Slattery scored 66 to finish another stroke back in fourth.
Lundberg won the Russian Open in 2005 and 2008.