Vanessa Hayden-Johnson and Daliborka Jokic each had 12 points for the Italian team, which trailed 44-37 early in the second half.
That's when the wheels came off spectacularly for Riga as Umana Reyer scored 20 unanswered points for a 57-44 lead with two minutes to go in the third quarter.
Riga battled back and twice closed the gap to just two in the final quarter but they never made it all the way and crashed to a third successive setback in the competition.
Simona Ballardini and Eva Giauro each poured in 10 points for Umana Reyer, while Mery Andrade and Aleksandra Vujovic scored eight apiece.
Umana Reyer were excellent at the free throw line, making 27 of 30 (90%).
Riga got a game-high 30 points from Essence Carson.
Ainars Cukste, coach TTT Riga:
"The third quarter was the decisive one; when we didn't play so aggressive like in the first half of the match. I congratulate Reyer Venezia for this victory, achieved mainly thanks to their very good defense".
Massimo Riga, coach Umana Reyer:
"We are happy to be on top spot in Group B. And I hope that we will play with the same intensity also in the Italian League. Now we have the possibility to reach the last-16 of EuroLeague and this is extraordinary for us".