After a tense 20 minutes with chances from both sides at PPL Park, Philly keeper Andre Blake could do nothing to prevent White's intervening header from a Scott Dann cross intended for Marouane Chamakh sail into the empty net behind him.
The Eagles then battled with a determined and exceptional Blake for the remainder of the game, with efforts from Yannick Bolasie, Joe Ledley and Dwight Gayle all being cleared.
Union made seven changes at the break and threatened to equalise on several occasions.
Palace struggled to maintain the same pace in the second half as they did the first, and Union maintain their danger to the end.
After a final chance from Sebastien Le Toux which very narrowly flew wide of the far post, Union were unable to grab a last-gasp equaliser and Palace clinched the victory.
Eagles manager Tony Pulis said the workout for the players mattered more than the result, but he thinks they should have won by a much greater margin.
"It was pleasing," the manager said. "We worked very hard, they made us work very hard. Full compliments to Philadelphia because it was a very competitive game.
"First half, truthfully, we should have scored quite a few goals and that’s not criticising them [Philadelphia] at all, that’s Bolasie, Puncheon, Chamakh and Gayley all missing really good chances that they should have scored from.
"In the second half, we made lots of changes and it was a good work out for us. That’s as hot as it’s been for the lads as well."
After a rain-splattered and cloudy victory over Columbus Crew on Thursday, Pulis was pleased the weather gave his players a greater challenge.
It’s onwards and upwards for the Eagles as they prepare for their final game on tour against Richmond Kickers on Monday night.
"As I’ve said before, the results don’t matter too much, it’s about getting the players fit," Pulis said.
“The fitness levels I think are pretty good and the lads just need more games now. The group will have more game time against Richmond.”
Crystal Palace kick off their 2014/15 season with a London derby away at Arsenal.