Evgeni Malkin scored a tying goal at 5:28 of the third, and Tristan Jarry made 22 saves for the Penguins (40-31-10), who had won three of four.
Pittsburgh remained one point behind the New York Islanders for the second wild card into the Stanley Cup Playoffs from the East with one game remaining for each. The Penguins will be eliminated from playoff contention if the Islanders get one point against the Montreal Canadiens on Wednesday.
"Anybody can beat anybody in this league. That's the reality," Pittsburgh coach Mike Sullivan said. "There's such a fine line between winning and losing. You have to be at your best every night. When you're not, you're going to run the risk of getting beat."
The Florida Panthers, who hold the first wild card, clinched a playoff berth with the Penguins loss and the Buffalo Sabres' 6-2 loss to the New Jersey Devils. With five fewer regulation wins than Florida, Pittsburgh can't pass the Panthers despite being two points back with one game left.
Petr Mrazek made 38 saves, Buddy Robinson had a goal and an assist, and Anders Bjork had two assists for the Blackhawks (26-49-6), who had lost three straight and 11 of 12. They lost 4-2 to the Minnesota Wild on Monday.
"The guys were just determined," Chicago coach Luke Richardson said. "I think we've played really good hockey as of late. We just couldn't get over that hump in the third period. Tonight, they were determined to get over the hump. A lot of credit. A lot of hard work out there."