Both players will sit out Game 4 in Tampa on Wednesday night.
Downie's ban comes as the result of a charge on Penguins defenseman Ben Lovejoy during the first period. He was going to be assessed a minor penalty on the play, but the Penguins scored a goal before the Lightning were able to gain possession of the puck for the whistle to be blown.
"I'm very disappoined in myself," Downie said Tuesday. "I felt like I let the team down."
Although Lovejoy said he was not hit in the head, NHL senior executive vice president vice president Colin Campbell said in announcing the suspension: "Downie left his feet and launched himself at the head of his opponent and he came from a considerable distance, with speed and force, to deliver the check."
Kunitz connected with an elbow to the head of Lightning forward Simon Gagne on a separate play in the first period of what ended up a 3-2 win for the Penguins. They hold a 2-1 lead in the best-of-seven series.
Gagne implied the blow was intentional, but Kunitz insisted it wasn't.
"I had my hearing this morning. Told my side of it. Obviously it looks bad. I never intentionally meant to hurt him. I'm glad that he's OK and was able to finish the game," Kunitz said.
The Penguins figure to feel the loss of Kunitz, who's one of their best offensive threats in the absence of Sidney Crosby and Evgeni Malkin.
"Right now, for our team, he’s playing on the top line both in a defensive situation matchup and an offensive situation," Bylsma said of Kunitz. "He is a power-play guy and a net-front presence guy, both on the power play and five-on-five. (He brings a) physicality factor to create room on the forecheck and in the offensive zone. He’s also a guy who can skate and add some speed to our lineup and straight lines to our game. He’s been able to add that depending on who his centerman is in different ways, but he’s been a pretty consistent performer in those aspects of the game. That would be something that he would be missing."