Evgeni Malkin and Radim Zohorna scored, and Tristan Jarry made 17 saves for the Penguins (2-3-0), who have lost two straight.
"We didn't play hard enough, and we didn't play smart enough," Pittsburgh coach Mike Sullivan said. "We got what we deserved.
"We had our chances, but give St. Louis credit. They defended hard, they took advantage of the opportunities we gave them. You know, we gave them way too many chances off the rush, because we didn't play with the purpose that we need to play with in the offensive zone, whether it be with the puck or without it."
Saad gave the Blues their first lead of the season, 1-0, at 9:33 of the first period. It took 199:33 for St. Louis to go ahead in its fourth game.
Malkin tied it 1-1 on a breakaway at 19:55 after coming out of the penalty box and being sprung by defenseman Kris Letang. It came after Blues center Brayden Schenn lost control of a puck near the goal line.
"I thought we had a good first," Neighbours said. "Obviously still things to clean up and stuff like that, but I thought we had a good first and it was just a bad bounce out of our zone at the end of a power play that had really a lot of good looks. It was tough, we knew that. It doesn't really deplete a team. We did a good job coming into the room and chatting about it, knowing that we had a good push there in the first and just needed to come out strong in the second."