Tursunov beat Germany's Nicolas Kiefer, 6-4, 3-6, 7-5, in a singles match and then teamed with Mikhail Youzhny for a 7-6 (7-2), 6-3 doubles win over Germans Christopher Kas and Philipp Petzschner.
That gave the Russians a 2-1 record in Blue Group round-robin play. While Italy, which defeated Spain on Friday, was also 2-1 in group play, the Russians beat Italy in their head-to-head match, earning a shot at the team title Saturday.
Sweden advanced to the championship by finishing the Red Group with a 3-0 record.
The title is to be decided Saturday in a best-of-three series -- two singles matches and a doubles match. Youzhny is to go against Sweden's Robin Soderling in one match while Russian Igor Andreev faces Thomas Johansson. The lineup for the double match was to be announced Saturday.
Russia has never won the ATP World Team title. Sweden is looking for its second championship, having won in 1995.