Akindele wasn't to be denied his goal as he handed the home side the lead in the 26th minute after he latched on to Blas Perez's clever chip over the top of the defence. The striker met the ball on the volley and smashed it into the bottom corner.
Philadelphia rallied towards the end of the first half and they got a goal back through Amobi Okugo, when he found the corner with an effort from close range after being found in the box by Cristian Maidana.
After the break, the home side regained the lead in fortuitous circumstances as Fabinho's attempted clearance in the box cannoned off Williams and flew past MacMath into the net, much to the bemusement of all the players on the pitch.
The Union tried to make a later push to find an equaliser late in the game, but the Dallas backline proved to be resolute.
Matters got worse for Philadelphia as they ended the game with 10 men when Maurice Edu was shown a straight red card for a challenge on behind on Perez, which allowed Dallas to ease to victory.