Fabian Castillo set up the goal, passing to Akindele for the easy tap-in.
It was Akindele's third goal in four games.
Castillo, who sat out the previous four games because of a suspension, nearly extended the lead in the 92nd minute with a shot that bounced squarely of the near post.
Chivas USA's best opportunity to draw even came when Erick Torres missed a header over the crossbar in the 78th minute.
“Today we played well but in soccer, it's who puts the ball in the back of the net,” Chivas USA Coach Wilmer Cabrera said.
Dallas (9-7-6) extended its undefeated run to seven games.
Chivas USA (6-10-5), which lost for the third consecutive game, took 13 shots to Dallas' 12 but only four were on goal.
Chivas USA was shut out for the sixth time.