The Fire responded to that threat and worked the ball well in the final third before Razvan Cocis tried his luck from the edge of the area, but his effort went over the bar.
Dallas almost took the lead before the break when Fabian Castillo raided down the left and fired a low shot at goal from inside the box, but Johnson was on hand to make a smart stop with his feet.
In the second half, Hollingshead came within inches of firing his side ahead when he latched onto Jair Benitez's cross into the box, but his left-footed volley struck the bar and went over.
The home side finally took the lead in the 83rd minute when Jeff Larentowicz's pinpoint cross into the box was guided into the bottom corner by Earnshaw's glancing header.
The Fire almost got a second goal when Quincy Amarikwa released the run of Earnshaw, but this time the former Nottingham Forest and Cardiff City man was denied by a good save from Fernandez.
Despite the Welshman's miss, the home side held out for just their fifth win of the campaign.