Dallas came even closer minutes later as Perez came within inches of putting his side with a shot which was cleared off the line by Paulo Renato.
In the second half, the Earthquakes responded to the pressure as they produced an opening for Chris Wondolowski on the edge of the box, but he put his strike just wide.
Dallas then upped the ante themselves as Tesho Akindele was played through down the right and he opted to go for goal, only to narrowly miss the target with a powerful shot.
The hosts forced the issue late in the game as Akindele managed to strike on target, but Bingham did well to keep out as the match looked to be heading for a draw.
However, in the dying seconds, Perez reacted quickly in front of goal to divert a close-range header past Bingham into the net and secure the three points for Dallas.