Versteeg took a pass from Brian Campbell, while standing in front of Penguins goalie Marc-Andre Fleury, and had his initial shot stopped. He got the rebound and knocked it past Fleury for his ninth goal. That lifted Chicago to its 10th win in 13 games (10-2-1).
"Anytime you go to the net, you're going to have to take a hit," Versteeg said. "I just was fortunate the puck kind of bounced out to me again."
Former Penguins forward Marian Hossa, booed every time he touched the puck, scored 7:37 into the game. It was his third goal in six games with the Blackhawks since he returned from a shoulder injury.
Jordan Staal tied it for Pittsburgh with 1:32 left in regulation after Niemi had stopped the Penguins' first 31 shots. Niemi, the backup to Cristobal Huet, fell just short of his third shutout in six starts this season.
"We just talked about how well he's played and he deserves maybe a little more ice time," Blackhawks coach Joel Quenneville said. "But it's nice to know that the tandem we have, the one-two punch is strong. He was great. It was a goalie win and he looked big, he looked confident, he found the puck. No rebounds, and he was in control.
"It was a pretty intense game."
The Penguins played without captain Sidney Crosby, who sat out because of a sore groin. Crosby had seven goals and four assists in his previous three games, all Pittsburgh victories.
Even without him, the talented teams had a bevy of young stars trading chances in an entertaining and physical game. There was a playoff feel in the matchup of two clubs with the second-best records in their conferences.
"It was a big game for both teams to prove themselves," Staal said. "Us coming into this game, we wanted to prove we could play with this team. We heard a lot about them and wanted to show them our best."
Hossa has been a villain in Pittsburgh since he left the Penguins and signed with the Detroit Red Wings two summers ago. Upon joining the Red Wings, the team that beat the Penguins in the 2008 Stanley Cup finals, Hossa said Detroit gave him the better chance to win a title.
Hossa's early goal Saturday almost stood up.
After Patrick Kane used his speed to gain the zone, Campbell took a shot from above the left circle. The rebound bounced off Fleury's chest and fell at the feet of Hossa, who came in from the right wing and scored.
"This is a huge win," Hossa said. "Obviously, we know how strong a team they have. We know [Crosby] didn't play, but without that key player they still have a talented team and they proved it. It was a tight defensive game, but we found a way to win, even when they scored last minute.
"It was a great game to watch."
Niemi was 1:32 away from making Hossa's goal stand until Evgeni Malkin's shot from the point hit a Chicago defenseman. The puck deflected right to Staal, who slammed it into an open net for his eighth of the season and second in two games.
"[Assistant coach] Mike Yeo had drawn up the play with a couple different options," Penguins coach Dan Bylsma said. "[Sergei] Gonchar made a great play and got it back to Malkin, and Staal was wide there going to the net and either looking for a pass or a rebound. And that's exactly what he got.
"You don't often get the opportunity to execute on of those faceoff plays, and we got one for a big point."
Pittsburgh, which came in having won three straight, six of seven and eight of 10, fell to 16-2-1 when having at least 30 shots.
Without Crosby, the Penguins had won 11 of their previous 14 -- and seven consecutive at home -- but they fell to 21-11-7 when he is out of the lineup.
"We came into this arena with high expectations of wanting to win," Versteeg said. "I think it was an exciting game. There were not too many goals, which is not very characteristic of these two teams. Overall, it was a well-played game on both sides.
"To come in and beat the Stanley Cup champs is special."
It was Chicago's first win in Pittsburgh since Feb. 22, 1997. ... Staal played in his 250th consecutive game, the fourth-longest streak in team history. ... The Blackhawks improved to 16-3-3 when scoring first, 11-1-1 when leading after one period, and 10-1 after 2. ... The Penguins had only 23 seconds of power-play time.