Victory on Sunday would clinch the Swede's third St Petersburg title.
Johansson, 31, who also won here in 1997, led 4-1 in the second set before the 128th-ranked Kunitsyn claimed the next four games to force a tiebreak.
The Swede, however, raced into a 6-0 lead in the tiebreak to secure victory.
Ancic broke the 204th-ranked Gulbis, making his ATP debut, twice in the first set and once more in the second.
The win over the 18-year-old Gulbis kept alive Ancic's chances of securing a spot at next month's season-ending Masters Cup.
He is 11th in the ATP Race with 349 points, 61 points behind eighth-placed Spaniard Tommy Robredo, who lost in the first round here.
The top eight are guaranteed a spot in Shanghai. Ancic will gain 38 points if he wins in St Petersburg.
Results:
Semi-finals: Thomas Johansson (Sweden) beat Igor Kunitsyn (Russia) 6-3, 7-6 (7-3); 3-Mario Ancic (Croatia) beat Ernest Gulbis (Latvia) 6-2, 6-3.
Quarter-finals: Kunitsyn beat Potito Starace (Italy) 6-3, 6-2; Ancic (Croatia) beat Max Mirnyi (Belarus) 6-4, 7-5; Johansson beat Wesley Moodie (South Africa) 6-3, 3-6, 6-3; Gulbis beat Jan Hernych (Czech Republic) 7-6 (8-6), 6-7 (4-7), 6-2.
GONZALEZ IN FINAL
BASEL: Chilean third seed Fernando Gonzalez powered into his third consecutive ATP final on Saturday with a 6-4, 6-4 Swiss Open semi-final win over Switzerland's Stanislas Wawrinka.
After making heavy work of his three previous matches in Basel this week, the world number seven seemed reinvigorated against the Swiss world number 40, taking control of the match with early breaks in each set.
Wawrinka, who downed Argentine second seed David Nalbandian in Friday's quarter-finals, had been hoping to set up an all-Swiss final with world number one Roger Federer but could find no way past the hard-hitting Chilean.
Federer, who beat Gonzalez in last week's Madrid Masters Series final, will take on unseeded Thai Paradorn Srichaphan in Saturday's second semi-final.
Results:
Semi-final: 3-Fernando Gonzalez (Chile) beat Stanislas Wawrinka (Switzerland) 6-4, 6-4.
Quarter-finals: Paradorn Srichaphan (Thailand) beat 7-Jose Acasuso (Argentina) 7-6 (7-2), 6-3; 1-Roger Federer (Switzerland) beat 5-David Ferrer (Spain) 6-3, 7-6 (16-14); Wawrinka beat 2-David Nalbandian (Argentina) 7-6 (9-7), 6-2; Gonzalez beat Juan Martin Del Potro (Argentina) 5-7, 6-4, 6-4.
LINZ OPEN
LINZ: Maria Sharapova defeated third-seeded Patty Schnyder of Switzerland 7-5, 7-5 on Saturday to reach the final of the Linz Open.
The top-seeded Russian will be bidding for her fifth title of the year.
Victory by Sharapova effectively ended Schnyder's hopes of joining the eight-player field for the WTA Championships that takes place in Madrid next month.
Sharapova's opponent in the final will be second seed and defending champion Nadia Petrova of Russia who defeated fourth-seeded Czech Nicole Vaidisova 6-1, 6-2.
It was largely a forgettable match, despite the closeness of the score. Schnyder did manage to move Sharapova around well but neither player managed to find rhythm or consistency.
Results:
Semi-finals: 2-Nadia Petrova (Russia) beat 4-Nicole Vaidisova (Czech Republic) 6-1, 6-2; 1-Maria Sharapova (Russia) beat 3-Patty Schnyder (Switzerland) 7-5, 7-5.
Quarter-finals: Schnyder beat Vera Zvonareva (Russia) 7-6 (7-2), 6-4; Sharapova beat 5-Ana Ivanovic (Serbia) 7-6 (7-3), 7-5; Petrova beat Samantha Stosur (Australia) 6-1, 6-3; Vaidisova beat 6-Jelena Jankovic (Serbia) 5-7, 7-6 (7-5), 6-4.
GROSJEAN STUNNED
LYON: Richard Gasquet defeated Robin Soderling 4-6, 6-3, 6-3 to set up an all-French semi-final against Arnaud Clement at the Lyon International on Friday.
Another Frenchman, Marc Gicquel, reached the last four with a 7-5, 1-6, 7-6 upset win over compatriot Sebastien Grosjean .
Fourth seed Gasquet, who is the highest seed left in the tournament following the exits of Marcos Baghdatis, Gaston Gaudio and Dominik Hrbaty, was overpowered by Soderling in the first set but came back strongly.
Clement, winner of the event in 2000 but now ranked 50th, outwitted eighth seed Nicolas Almagro of Spain 6-3, 6-2.
In the other semi-final, Gicquel will face seventh seed Xavier Malisse. The Belgian beat American Robby Ginepri 6-4, 6-3.
Results:
Quarter-finals: 4-Richard Gasquet (France) beat 5-Robin Soederling (Sweden) 4-6, 6-3, 6-3; Arnaud Clement (France) beat 8-Nicolas Almagro (Spain) 6-3, 6-2; Marc Gicquel (France) beat 6-Sebastien Grosjean (France) 7-5, 1-6, 7-6 (7-5); 7-Xavier Malisse (Belgium) beat Robby Ginepri (US) 6-4, 6-3.—Reuters