Thompson poured in 24 points and Diana Taurasi added 23 as the star-laden Russian outfit prevailed 76-62 on their home floor to win the title for the first time.
Thompson, playing her first season in Europe, was voted as the Final Four MVP and also surpassed Delisha Milton-Jones of Ros Casares as the league's leading scorer this season.
"I'm very excited about the win," Thompson said. "It was long road.
"We had to beat Samara (in the semi-final), who had beaten us three times this year and to beat them, we had to play perfect.
"We came out persistent with a lot of poise tonight and did what we had to do to win."
Playing in front of more than 4,000 fans, Spartak stormed out to a 37-22 lead late in the first half but the Valencia team battled back with Thompson's fellow USA international Milton-Jones leading the way.
Milton-Jones scored nine of her team-high 21 points in a spurt that closed the gap to 43-42 with 3:10 remaining in the third quarter.
Ros then had a chance to take the lead after Tamika Whitmore missed from 15 feet but Spartak's defense held firm.
Allison Feaster-Strong turned the ball over after stepping on the out-of-bounds line under the basket, and the Russians then pulled away.
Thompson hit a jumper and Whitmore made a lay-up to force Ros coach Manolo Real to call a timeout.
When play resumed, back-up point guard Marina Karpunin scored a lay-up and Ticha Penicheiro sank two free throws.
Thompson then split two from line and Whitmore buried a jump shot to complete an 11-0 run to give Spartak a 54-42 lead.
Ros attempted to come back again.
Midway through the final quarter, Erika De Souza grabbed the offensive rebound after a missed three-pointer by Allison Feaster-Strong and scored to close to within 61-55.
Fouled on the play, the Brazilian international Erika went to the charity stripe but missed, and Spartak put the game away for good with another 6-0 run that was capped by a Taurasi jumper.
Thompson finished nine of 15 from the floor, including four of seven from the arc, while Taurasi was nine of 13 from the floor, including four of six from three-point range.
Milton-Jones, who fouled out late, got great support from Spanish international Laia Palau, who had 11 points and played terrific defense.
Ros Casares' long-range shooting let them down as they finished four of 21 with Elisa Aguilar, another Spain national team star, four of 10.
In the third place game played earlier in the day, CSKA Volgaburmash defeated Bourges Basket 68-59 despite a game-high 24 points by Evina Maltsi.
Amaya Valdemoro led CSKA with 23.
Solheim Cup 2019
The Solheim Cup