Robbie Keane should have done better with an effort in the 35th minute when he collected a loose ball inside the penalty area, but he was not able to keep his volley down as it skied over the crossbar.
After half time, Fernandez kept his side in the game with a great double save to first deny Sean Franklin's low effort from the right and then a rebound strike from Rogers, as the Dallas defence then hacked the ball clear off the line.
The keeper was in inspired form as he was called into action yet again, this time to stop Gyasi Zardes's header from Jimenez's cross finding the net.
However, the pressure on the Dallas goal finally told as Sarvas headed the ball into the net from Keane's left-wing cross, with Fernandez helpless in the 65th minute.
Galaxy made sure of the points in the 80th minute when Rogers raided down the left and played the ball low back into the middle of the box for Jimenez, who slotted it home.