Russia will now meet France, who beat the Czech Republic 71-68, for a spot in the gold medal match.
The rematch of last year's EuroBasket final went Russia's way again when a three-point attempt by Turkey's Birsel Vardarli bounced off the rim as time expired.
Turkey's women, in their first Olympics, were one of the surprise teams in the preliminary rounds, posting a 4-1 record with their only loss coming against the powerhouse U.S. team.
"I think today was a really equal game," said Russia coach Boris Sokolovskiy, whose team had a 3-2 record in qualifying. "I think we were luckier. I've seen Turkey progress a lot."
The teams entered the fourth quarter tied at 51-51 and the game came down to a close struggle over the final seconds.
Russia's American-born point guard Becky Hammon drove through Turkey's defence for a lay-up that snapped a 62-62 tie with 14 seconds left.
Kuanitra Holingsvorth missed one of two free throws to leave Russia with a one-point lead. Holingsvorth then lost a rebound out of bounds and that led to Turkey committing two fouls and Russia making two free throws for a 66-63 lead.
With 10.5 seconds left, Turkey had a chance to stay alive with a three-pointer, and Vardarli, who had made 2-of-3 from beyond the arc, got a good look but failed to sink it.
"If we would have won, we would have had a chance of a medal. That is how important this game was," said Turkey coach Ceyhun Yildizoglu.
"Our goal is to make the Turkish people proud of us. I believe in the future we will do really great things in the Olympics."
Shot statistics backed up how tight the game was with Russia making 25-of-60 shots and seven three-pointers while Turkey was 24-of-59 with six three-pointers.
Russia were led by naturalised Russian citizen Hammon, who scored 19 points.
Nevriye Yilmaz was Turkey's top scorer with 22 points.
France roared back from an 11-point deficit in the fourth quarter to overtake the Czech Republic and book their spot in the semis.
Led by the inspirational play of point guard Celine Dumerc, France came back after trailing 55-44, taking a 67-65 lead they would not relinquish on a three-poiner by Dumerc with one minute to play and stayed alive in their pursuit for an Olympic medal.
"We beat a really, really good team," said France coach Pierre Vincent. "I don't know where we found the energy and the confidence to come back in this game. I don't know. Ask Celine."
Dumerc, sitting next to her coach at the news conference, said she and her team-mates just dug deep.
"We had to keep our mind focussed on what we had to do and we found a way to score a basket. I don't know where we found the energy and I'm really, really proud of my team."
Dumerc finished with 23 points to lead France. Eva Viteckova scored 17 points as top scorer for the Czechs.
The Czechs had used a brilliant scoring outburst from Viteckova to take a 51-41 lead after three quarters. Viteckova, held scoreless in the first half, accounted for 13 points in the quarter.
After Dumerc led France back, she was able to run the finals seconds off the clock and just before the buzzer threw the ball high up in the air and hugged her team-mates, all of whom then collapsed to the floor in a group celebration.
France's turnaround began with intensified defensive pressure that finally cooled off the Czechs' hot shooting.
The 5-foot-6 Dumerc, 30, said she appealed to her team-mates.
"Just keep running, keep fighting, keep believing in what you are doing," the charismatic player said. "I said to my team-mates, 'we don't want to be crying at the end.'"
Dumerc, who saved France from an upset against Britain earlier in the tournament by sinking a three-pointer to send that game to overtime and another three-pointer to win in the extra period as time ran out, said the Olympics was bringing out her best.
"It's like I'm dreaming. The last shot I scored, I was like, 'again?' Every day I am waking up and thinking I am at the Olympics. And this is making me feel so good and so happy.
"Even if I am tired, I look around and see all these rings everywhere and these athletes. All these special (things) for sport and that is who I am. I love to play the game."
In the other women's semi-final, four-time Olympic defending champions the United States will play Australia, who have lost to the Americans in the last three Olympic gold medal games.
The Americans defeated Canada 91-48 to extend their Olympic winning streak to 39 in a row, and Australia were 75-60 winners against China.
The semi-final winners will advance to the gold medal game and the losers will play for the bronze.