Mauro Diaz, who assisted on both goals, set up Akindele with a diagonal cross from near midfield.
Blas Perez pulled FC Dallas (6-2-2) even in the 77th minute, slipping past goalkeeper Jaime Penedo for an open net finish. Diaz floated a chip pass over the Galaxy defense to create the space for Perez.
FC Dallas remained first in the overall MLS standings, tied with the Vancouver Whitecaps.
Gyasi Zardes opened the scoring in the 59th minute, redirecting Stefan Ishizaki's corner kick with a header.
Ignacio Maganto had a goal for the Galaxy (3-3-5) disallowed in the 40th minute after referee Kevin Stott ruled that the Tommy Meyer was in an offside position when he obstructed the sight line of goalkeeper Dan Kennedy.