Diana Taurasi poured in a game-high 31 points and her fellow USA international Sue Bird contributed 13 with 10 assists as Spartak prevailed 85-70.
Avenida battled from start to finish and got 25 points from Le'Coe Willingham but Spartak, with Taurasi, Bird, stifling team defense and superb rebounding, won the day.
Taurasi, who also had 33 points in Spartak's Semi-Final triumph over UMMC Ekaterinburg, was voted as the Final Four MVP.
|Diana Taurasi also took home the tournament's MVP title|
"I'm really happy," Taurasi said.
"It's not easy to win three EuroLeague titles in a row, but we have done it. It's been a difficult season for us, but this makes it all worth it."
UMMC Ekaterinburg loaded up their team with international superstars as well and beat Spartak in the final of the Cup of Russia.
The EuroLeague Women has been owned for three seasons by Spartak, though.
The Moscow Region team also got terrific performances from Sylvia Fowles, Lauren Jackson and Marina Karpunina and Kelly Miller.
Spartak, who out-rebounded Avenida 43-30, took control in the second quarter when they outscored Avenida 24-13 for a 46-34 lead at half-time.
Leading only 26-23, Bird hit a three-pointer before Taurasi stole the ball away from Avenida's Silvia Dominguez and passed up the court to an open Karpunina who made a lay-up and drew a foul by Gunta Basko on the play.
Karpunina sank the free throw for the three-point play to give Spartak a 32-23 advantage.
Avenida never got closer than seven points the rest of the way.
"Spartak are true champions," said Isa Sanchez of Avenida.
"They were very strong. But we're extremely proud of what we've done. We stayed in the game and we've had a really good tournament.
"We are an ambitious team and we hope we can repeat this."
Spartak had to survive a tough Quarter-Final series with Ros Casares, winning that 2-1 just to reach the Final Four, while Avenida overcame CSKA Moscow 2-1 in their Eighth-Finals showdown before sweeping MiZo Pecs 2010 to advance.
"It's fantastic to win a third consecutive title," Bird said.
"We've made history and now we must enjoy what we've achieved. It's been a great atmosphere, a fantastic crowd.
Hungarian coach Laszlo Ratgeber, who took the reins of Spartak last summer, said: "Taurasi is the most exciting player in the world. Sue Bird was just fantastic, and Lauren Jackson.
"It was a great team effort. This was our aim coming into the season and we are the strongest."
Tempers flared in the fourth quarter with Sanchez and Taurasi exchanging words, with the home crowd showering boos on Taurasi.
But the USA international who hit five of 10 shots from three-point range and came up with six steals, had only nice things to say about Salamanca and their fans after the final buzzer.
"We've had a really good weekend in Salamanca and the fans and the atmosphere has been amazing," she said.