Trailing 65-50 at the start of the final quarter, Spartak reeled off 11 unanswered points, cutting the gap to four when Sylvia Fowles sank a jump-shot with 5:57 left to go in the contest.
Erika De Souza got a tip-in from Amaya Valdemoro's missed lay-up, but it only temporarily stopped the bleeding for the hosts as Spartak scored another six unanswered points, tying the game on Lauren Jackson's jump-shot with 2:52 left on the clock.
Valdemoro put Casares back on top with two from the free-throw line, but Diana Taurasi hit right back with a lay-up.
Valdemoro missed a jump-shot but Spartak could not capitalise as Sue Bird was off the mark with a three-point at the other end.
That allowed Casares to pull back in front as Kelli Miller fouled Valdemoro to send her back to the line, where she sank both shots.
Taurasi missed a jump-shot for Spartak and Valdemoro extended the home lead to four with a jump-shot 46 seconds from time.
Taurasi cut the gap back to two with a pair from the charity stripe after a foul was called on on Laia Palau, and Spartak had the chance to tie or win it after Valdemoro missed a jump-shot and Fowles grabbed the rebound with six seconds to go.
But as they raced to the other end, Palau reached in to steal the ball away from Bird and win it for Casares.
Valdemoro had 21 points for Casares while DeLisha Milton added 16 and eight rebounds while De Souza finished with 11 points.
Taurasi's massive 33-point haul went to waste for Spartak, as did 14 points and 11 rebounds from Fowles.
The two teams will now try again in Game Three in Vidnoje, Moscow Region on Wednesday night, where Spartak were 65-57 winners last Tuesday.
László Rátgéber (Spartak Moscow Region):
"First of all I would like to to congratulate Ciudad Ros Casares and their fans, because they created a big party. I don't know if these two teams are the best teams in EuroLeague, but I'm in the EuroLeague since 1996 and I can tell you they play really good. It's difficult for me to speak after that last action."