The Earthquakes took the lead in the eighth minute when Alan Gordon fired Cordell Cato's cross into the penalty area past Raul Fernandez into the bottom corner.
San Jose doubled their lead eight minutes later when Steven Beitashour surged forward from right back and latched onto Rafael Baca's lofted pass and volleyed over Fernandez and into the net.
However, Dallas got a goal back almost immediately when Blas Perez tapped the ball home from close range after reacting first to a loose ball in the penalty area.
San Jose almost retook the lead when Steven Lenhart headed Jordan Stewart's cross at goal but Fernandez was on hand to make the save.
The game ended in tumultuous fashion as the visitors were reduced to nine men within five minutes as Justin Morrow was given a straight red card for a late challenge.
Meanwhile Bernardez was given a second yellow for an altercation with Dallas striker Kenny Cooper, which also saw him given his marching orders, as the game ended all square.