Dallas (5-5-2) was on the verge of a franchise-worst fifth consecutive loss before Castillo scored. Jair Benitez sent a second-effort cross to Castillo immediately after a corner and the midfielder poked the ball past goalkeeper Dan Kennedy.
Marco Delgado scored his first career goal -- a day after his 19th birthday -- in the 60th minute for Chivas.
Despite the recent losing streak and necessity for late heroics, Dallas Coach Oscar Pareja expected to get a victory against lowly Chivas (2-5-4) and was disappointed for his team.
“We worked hard to bounce back today. The game became complicated after Chivas scored in the second half,” said Pareja, whose team had the best record in MLS before the losing streak. “First half, we managed the game. We had some options with the penetration that I would like to see from this game, but the game was controlled.
“I knew from the first minute that Chivas was going to sit back and wait for any mistake in the back and that's what happened in the second half.”
Delgado's goal came after Dallas controlled the ball, finishing with 62.4% of the possession, but failed to break the deadlock in the first 60 minutes.
Delgado, who made his debut in 2012, capitalized when Mauro Rosales beat Dallas leftback Michel on the right side of the box and fed the ball to the 19-year-old for a one-timed goal.
The strike came after Martin Rivero switched the point of attack from the left side of the field to the right, taking advantage of a rare Dallas miscue in the back.
“I've worked hard all my life ever since I was a youngin',” Delgado said, “and to get to this point and to finally get my first MLS goal, I couldn't really celebrate — I didn't really know what to do. I just wanted to go down in tears.”
His first goal looked as if it would hold up until Dallas amped up the pressure in the final 10 minutes. Dallas had 10 shots in the second half, with a flurry of them in the final sequences as the hosts grasped for three points.
Chivas also wanted to leave a winner, but Coach Wilmer Cabrera was satisfied with a road point. His team logged just its second win of the season last weekend.
“It's not easy to get a point on the road and we've gotten four points on the last two games on the road,” Cabrera. "It is important to continue to believe in what we do and for the players to continue working.”