Going up against a team that has been a thorn in their side in Russia this season, Spartak's Diana Taurasi underlined her status as one of the world's most exciting players by scoring 33 points.
Sue Bird hit three big shots in the fourth quarter on her way to 17 points.
Spartak will now face the winner of the second Semi-Final between hosts Halcon Avenida and MKB Euroleasing Sopron.
Agnieszka Bibrzycka had an outstanding game for Ekaterinburg with 23 points but UMMC had no answer for Taurasi all game long, and definitely not for superstar Bird who made game-winning contributions on both ends of the floor.
"We simply couldn't stop some of their players like Diana, Sue," Bibrzycka said. "We're very disappointed but we will meet Spartak again in the Russian league and we hope to beat them and become the Russian champions.
"This will give us extra motivation to beat them. I want to congratulate them because we played a very good game. I also want to say thanks to all of our fans who showed their support by coming here."
Laszlo Ratgeber, the Hungarian national team boss who was handed the Spartak reins late in the summer, celebrated as if his team had won the final.
"The defense by my team in the second half was outstanding," he said. "That's what I'm most proud of."
No player was more crucial in that regard than Bird, who had the tough assignment of guarding Ekaterinburg playmaker Cappie Pondexter, her teammate on the USA Olympic gold-medal winning team last summer in Beijing.
Ekaterinburg and Pondexter were at their most dangerous when putting the ball on the floor and driving to the basket.
In one key moment late in the third quarter, just after Bird had buried a jump shot for a 64-55 Spartak advantage, Pondexter dribbled on the left, lowered her shoulder and collided with Bird who went to the ground.
The referee called a foul on Pondexter.
Bird was injured on the play and had to be helped off the floor.
Ekaterinburg stayed within striking distance and closed to within 67-66 three minutes into the final quarter after two Penny Taylor free throws.
Vetra's team had two chances to take the lead but Spartak's defense forced UMMC to kick the ball outside to Nolan who missed a three from the corner in front of Ratgeber's bench.
On the next trip down the floor, the excellent Russia international Tatiana Shchegoleva stole a pass from Sandrine Gruda.
Fifteen seconds later and Bird, who had checked back into the contest, connected from behind the arc for a 70-66 lead.
After Nolan was off target from 15 feet, Taurasi hit a jumper.
Maria Stepanova reduced the arrears to 72-68 with a free-throw line jump shot, but Bird hit back-to-back jumpers and Taurasi followed with another to open an eight-point lead.
Spartak held on for the win.
Sylvia Fowles had moments when she dominated in the low post for Spartak and finished with 14 points and a game-high nine rebounds.
Lauren Jackson scored 11.
Spartak were a perfect 10 of 10 at the free-throw line at half-time and ended the game 13 of 13 while UMMC were 19 of 23.
Gruda, the France international, had 12 points and eight rebounds while Nolan scored 13. Pondexter played more than 39 minutes before fouling out with 10 points and eight rebounds.