Marc-Andre Fleury made 42 saves, and Jujhar Khaira and Seth Jones each scored his first goal with the Blackhawks (3-9-2), who won 2-1 in overtime against the Nashville Predators here on Sunday.
King replaced Jeremy Colliton as coach Saturday. Colliton was fired after going 87-92-26 in four seasons as Chicago coach.
"Winning makes everything better," Jones said. "But it comes at a price, and that's hard work. I think we've started doing the little things, as you can see, in our game in the defensive zone, blocking more shots, stopping a defensive zone, winning more puck battles to create battles in the neutral zone. And once we're in the offensive zone, it's easy.
"You can be creative, but you have to put the work in the other two zones first, and I think that's what's making us successful these last couple of games."
Jeff Carter forced overtime with two goals in the third period for the Penguins (4-3-4), who have lost five of six but are 1-0-2 in their past three games. Tristan Jarry made 30 saves.
Pittsburgh played a third game without center Sidney Crosby and coach Mike Sullivan, who are in NHL COVID-19 protocol. Penguins assistant Todd Reirden assumed Sullivan's duties again.
"That was a great response by our team," Reirden said. "I don't think we were overly pleased with how the first two periods went. I thought our urgency and desperation went to a different level. That was one of our stronger periods of the year. I was really happy with our third period."
Khaira gave Chicago a 1-0 lead at 2:14 of the second period when he took a pass from Jonathan Toews in front of the net and shot it past Jarry. Khaira played his first six NHL seasons with the Edmonton Oilers.