Downie and Kunitz handed one-game bans for head shots
Kunitz was banned for elbowing Lightning forward Simon Gagne during Monday's game while Downie earned his suspension for leaving his feet to deliver a crushing hit on the Penguins' Ben Lovejoy.
Both players were assessed minor penalties.
The two players will serve their suspensions when the best-of-seven series, which Pittsburgh leads 2-1, resumes Wednesday in Tampa, Florida.
(Reporting by Steve Keating; Editing by Frank Pingue)