The 33-year old attacker scored a stunning 59th minute volley to cancel out David Ferreira's opener before producing a stealthy cut-back and cross to force Dallas defender Matt Hedges to divert the ball into his own net.
Rapids head coach Oscar Pareja was thrilled with the performance from Sanchez who has become a key ingredient in his line-up since crossing from Nacional in early August.
"That's why Vicente's here," Pareja said of Sanchez.
"The people are getting in love with [Sanchez], and most important is that his teammates are yelling with him and Gaby [Torres]. These guys know that coming to this locker room means there is no egos, no one is bigger than this club."
Sanchez added: "I'm happy because this is what we've worked to all season. These are playoff games that we have to win.
"It was a complicated week, a very complicated week for Colorado. It was good to give a little happiness to the crowd."