Morrow's 12th goal this season knotted the contest 1-1 at 4:52 of the second period after assists by Ribeiro and Matt Niskanen.
Ribeiro's 16th came at 10:44 of the second following assists by Morrow and Sergei Zubov and gave Dallas a 3-2 lead.
San Jose's goals were scored by Devin Setoguchi in the first and Patrick Rissmiller in the second.
Goaltender Evgeni Nabokov made 18 saves on 21 shots for the Sharks, who had won six of their previous seven games.
They fell to 6-7-2 at home this season.
Both teams went 0 for 5 on the power play.