Ralph Mims again led Roanne with 25 points, including four of seven three-pointers, with David Noel adding 17 for the visitors.
APOEL were led by 17 Brandon Heath points as their Final Four appearance dream ended.
Rashid Atkins gave the home side the lead with a score from outside the arc, but a tight first period saw several lead changes before Noel's dunk sent Roanne into the first break with a 25-23 lead.
Roanne started the second period well, and a pair of Noel free-throws made it a double digit lead at the midway point before the same player hit a jump-shot to make it 39-27.
The visitors remained in control, and despite Milan Dozet converting a lay-up with 45 seconds remaining, Roanne went into the locker room 49-37 ahead.
It was still an 11-point game heading into the final four minutes of the third period, but APOEL reeled off seven straight points to get back into the game, and it took a Papa-Phillippe-Amagou free-throw to put Roanne 63-61 up heading into the final break.
Mims sunk a trey to open the fourth period for Roanne up by five, but the home side refused to go away, and a driving lay-up from Heath made it a one point game, 75-76, with 4:31 on the clock.
That proved to be as close as the home team came, and a Page's dunk of Mims' assist effectively wrapped things up and sent Roanne into the Final Four.
"We won but it was not easy. [That was a] great game tonight. We knew it was going to be difficult but we did it and now are going to the Final Four."
Ralph Mims, Roanne player:
"We played a good game tonight. We played against a good team. We came and we did what we had to do."
Yiannis Christopoulos, APOEL coach:
"Congratulations to Roanne. We should have done a better job. We battled in the second half but we made some mistakes and lost the game. Now we hope to do well in our domestic league."
Gerben Van Dorpe, APOEL player:
"It was a very tough game for us. Congratulations to Roanne. They were the stronger team. We had some problems finishing the points. Good luck to Roanne [in the Final Four]."