The Hammers had a 2-1 lead when play was temporarily suspended on the hour mark due to the weather, but ended up suffering their second defeat in the United States when Marvin Ceballos converted from the penalty spot.
In the 13th minute the hosts went in front when West Ham defender Winston Reid turned the ball into his own net while trying to clear a cross into the box.
The 28-year-old managed to redeem himself five minutes later, though, as he scored at the other end after receiving the ball from Andy Carroll.
As well as bagging an assist, Carroll got on the scoresheet himself as he connected to Sofiane Feghouli's cross before sending the ball into the back of the net.
Five minutes after play was restarted following a lengthy delay, the Railhawks hit back after a penalty was awarded for Lewis Page's handball in the box.
Ceballos sent goalkeeper Raphael Spiegel the wrong way, and matters got worse for West Ham when Doneil Henry was forced off the pitch with an injury, leaving the team with just 10 men in the final five minutes.