Ribeiro tucked a power-play rebound by Phoenix goaltender Mikael Tellqvist for his 13th goal of the season as Dallas improved to 5-1 in its past six games.
Sergei Zubov gave the Stars a 4-3 lead with 4:24 remaining in regulation, scoring his 11th of the season from the right circle.
But Shane Doan tied it at four with 1:33 left in regulation while the Coyotes had a five-on-three. Phoenix was able to add a sixth attacker when Dallas was called for a delayed penalty.
Niklas Hagman and Brenden Morrow also scored for the Stars. Morrow was playing his second game since returning from severed tendons in his wrist that kept him out since Dec. 26.
Fredrik Sjostrom, Derek Morris and Mathias Tjarnqvist added goals, and Tellqvist stopped 23 shots for the Coyotes, 1-7-1 in their past nine.