Konstantinos Charalampidis poured in 18 points, including 13 in the first half when the Greek team took command.
Devin Smith finished with a game-high 25 points for Panellinios, who host the second leg on October 27.
Panellinios began the contest in electric fashion, reeling off the first nine points with Roderick Blakney, Ian Vougioukas and Charalampidis all scoring.
VEF Riga hit back immediately.
A Jurijs Aleksejevs jump shot closed the gap to 11-10, but the first half belonged to the visitors.
They blew the game wide open with a 23-8 run that bridged the first and second quarters and left them on top at 39-20 with 5:12 remaining in the half.
Charalampidis poured in seven points during that surge.
With 3:15 to go in the second quarter, VEF Riga showed signs of a recovery.
Janis Gailitis and Aleksejevs drilled back-to-back three-pointers, and the pair added two more baskets to reduce the arrears to 44-35.
They went to the break trailing 49-37, however, after a three-point play by Blakney.
The Riga team's chances didn't look good when play resumed as Vougioukas dunked and Charalampidis followed with a three-pointer for a 54-37 Panellinios lead.
In fact, they stayed in front by double digits the rest of the way.
Twice they went in front by 20 in the fourth quarter, though VEF Riga did make a last-ditch effort to claw their way back.
An Arnas Labuckas lay-up trimmed the deficit to 84-73 with 3:17 remaining, but the hosts got no closer.
Djuro Ostojic dunked and Smith buried a three-pointer to take the advantage to 89-73 with 2:16 to play and they ended up winning by 15.
Aleksejevs had 21 points for VEF Riga.
Panellinios coach Ilias Zouros:
"This was very important game for us, in addition to it being our first official game of the season. We hoped for the win but we were still cautious because we have a lot of new players and we still need to find our game; so I'm very happy with this win. VEF Riga is a dangerous team with very good perimeter players so we have to keep in mind that this is only half time..."