Spalletti leads Zenit to Russian Cup success
Midfielder Roman Shirokov scored with a 60th-minute penalty to settle the game played in the southern city of Rostov, the first Russian Cup final played outside Moscow.
Zenit dominated the match but Premier League newcomers Sibir, playing their first cup final, missed a great chance for an equaliser in added time.
St Petersburg's Belgian defender Nicolas Lombaerts cleared a goal-bound shot off the line to help his team to their third cup triumph and first since 1999.
"I would like to congratulate our fans for helping us win this match," Spalletti told reporters. "It was a tough game and Sibir was a worthy opponent but we fully deserved our victory."
Spalletti, named Zenit coach in December after quitting Serie A side AS Roma, now has a chance to win the league and cup double in his first season in St Petersburg.
Zenit top the standings by a point with the March-November Russian league taking a seven-week break for the World Cup.