The home side came into game three of their Eighth-Finals Playoff series with Bourges needing a win to keep their hopes alive of making a second straight Final Four.
Both teams came out sluggish on offense, but Bourges had Endene Miyem to rely on as she scored her team's first eight points.
Avenida meanwhile struggled mightily, especially their leader Sancho Lyttle who was frustrated by the physical play of the Bourges defense, and showed it on several occasions looking skyward in disbelief.
An Ana Lelas turn-around jumper from the baseline for Bourges gave her side a 14-5 advantage and Avenida were out of sorts.
The girls from Salamanca would make some noise however before the first quarter ended.
Lyttle finally got on the board with a pair of free-throws at the 1:37 mark, and a minute later she managed her first field goal. A Sylvia Dominguez coast to coast lay-up as time expired found the home team down just 14-11 with 10 minutes gone.
It looked as if the home side was in the process of resting control of the game early in the second, but Bourges responded.
A Paoline Slagnac three-pointer made it 19-15 and the French used great ball movement to score on two straight possessions and widen the gap to 23-15.
Moments later Styliani Kaltsidou stole the ball and streaked down the court, missing a lay-up. But Miyem was there to collect the rebound and give her team a 25-15 edge.
The lead would go to 29-15 before Sylvia Dominguez stopped the bleeding with a jump shot. Her team outscored their opponents 5-3 the rest of the way to go into the half-time break down by a manageable 10 points.
With the third quarter half way gone Avenida made their move.
Lyttle cut the lead to 10 with a bucket at the 6:41 mark igniting a 14-0 Avenida run that ended with an Ana Lelas jumper inside of two minutes.
Anke DeMondt responded by burying a three-pointer to make it 40-37.
Still Bourges hung in and managed to go into the final quarter with a 41-40 lead.
Avenida continued to apply pressure as the fourth quarter got under way, but the girls from Bourges would not fold, with the lead changing hands on nearly every possession.
Alba Torrens gave her team a 50-47 edge with 6:55 remaining, and the Avenida defense followed by forcing a backcourt violation but they failed to capitalize on the other end.
The hero for Avenida would be the diminutive point guard Sylvia Dominguez.
The 1.67m sparkplug was all over the court, grabbing rebounds over much bigger players, and slashing to the basket where she would either draw a foul or put two on the board. Her runner with 37 seconds left gave her team a 60-53 lead and only the foul line stood between Avenida the Quarter-Finals from there on out.
Jordi Fernandez, Halcon Avenida coach:
"After a bad first half, we worked very hard in defense stopping their best players. Maybe we need to be more fresh and try to find for better options in offense."
Sancho Lyttle, Halcon Avenida player:
"We played better in second half, offensively and defensively. It's a very important and deserved victory."
Pierre Vincent, Bourges Basket coach:
"We played a big game, especially in defense but to win in Salamanca a team must be perfect. We missed some important shots in the last few minutes."
Ana Lelas, Bourges Basket player:
"It's very hard when you lose after playing like we did today. We are proud for the job we did. Both team deserved to be in the next round."