The Russians led 20-19 at the end of the first quarter but then turned on the style, all but sealing their place in the next stage of the competition.
It will take a monumental effort from Panionios to claw back the 23-point deficit.
The chief destroyer for Moscow was Plenette Michelle Pierson, who had 25 points.
Monique Currie was also in good form, pouring in 21.
Extrugasa defeated Electra Ramat-Hasharon 60-54 in the last game to finish on Thursday, but they might have had a more convincing victory were it not for the fighting spirit of the Israeli team.
The Spanish side had a 10-point lead at the start of the fourth quarter but will now have to go to Israel trying to protect it in what is a very intriguing second leg scheduled for February 7.
Agne Ciudariene had 15 points in the victory, while Rada Vidovic scored 17 and grabbed 10 rebounds in defeat.