Haula converted Ryan Dzingel's feed from behind the net to tie it 3-3 at 10:59.
Blackwood, who made 28 saves in the loss to the Flyers, improved to 3-2-3.
"I haven't necessarily played from the start of the season until now the way I want to," he said. "But every day is a battle, and I'm trying to find consistency in my game and string a couple good starts together."
It was the first of a five-game road trip for the Devils, who played eight of their first 11 at home, including the previous six.
"(We won) one now on the road, so we've got to keep going," Hischier said. "We needed that win, big time. It's good for our confidence, good for the team."