Guentzel tied it 2-2 on a one-timer from the slot off a feed from Crosby 27 seconds into the third period.
Lucas Raymond scored the only goal in the shootout in the first round. Guentzel shot wide, and Pickard made saves against Crosby and Kris Letang.
Smith gave the Red Wings a 1-0 lead at 18:19 of the first period. After a shot from Sam Gagner produced a rebound, Smith spun off Penguins defenseman John Marino in front of the crease for a backhand.
Guentzel tied it 1-1 with a power-play goal at 5:54 of the second period, scoring on a rebound off a slap shot from Crosby that hit Evgeni Malkin in front. The goal ended Guentzel's three-game point drought, which was his longest this season.
"We knew we needed to take another step in the second period there," Guentzel said. "I thought we did that. I thought we controlled the play and got to the front of the net, which we needed to do to try to disrupt their goaltender."
Zadina scored on a power play to give the Red Wings a 2-1 lead at 16:31. Nick Leddy shot into traffic and Zadina scored on a wrist shot near the crease before Marino could make a clear.
"I'm not saying we outplayed them," Detroit coach Jeff Blashill said. "They certainly had their chances. But I think we did a lot of things that you have to do in order to beat good teams, have a chance to beat good teams and to win on the road. I thought we did a much better job of managing the puck. Much, much, much better.
"Certainly, weren't perfect. They had a lot of chances. They're a good team. But I thought we did a real good job of that."