The FC Dallas attacker redirected a cross for a goal, ruining a dream debut for the Chivas USA teenager.
In the 60th minute, Delgado, a day removed from his 19th birthday, scored his first professional goal thanks to a Mauro Rosales cross. The Argentine was able to juke his way past FC Dallas left back Michel after receiving a long pass from Martin Rivero.
It looked like that might be the only tally, but Dallas ramped up the pressure in the last 10 minutes and found a goal in the 83rd when Jair Benitez's left-footed cross took a deflection and found its way to the feet of Fabian Castillo, who directed it over the goal line.
The home crowd thought the match was won in the final minute when a set piece found the head of defender Stephen Keel, who played it to an eager teammate who finished, but the assistant adjudged the play to be offside.
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The goals came after a lifeless first half that saw Dallas manager Oscar Pareja switch from a 4-2-3-1 formation to a 4-4-2 in a fruitless search for an attacking spark from his club. On the plus side for the home manager, Dallas' opposite number was even less effective in attack, managing only one shot — a Rosales effort that went wide.
The draw prevents Chivas USA from starting a win streak after a 3-1 triumph over Colorado last time out. Honduran winger Marvin Chavez scored twice in that match but missed Saturday's game, as he is already in Florida with the national team training for the World Cup.
Dallas has no international absences but is without playmaker Mauro Diaz and defensive midfielder Hendry Thomas because of long-term leg injuries. The result snapped a four-match losing streak for the hosts.