Time was ticking down in the second period with the Penguins trailing 2-1, but Kunitz tied it just 14 seconds from the intermission. It was his 18th goal of the season.
Sutter put Pittsburgh in front 1:46 into the third and Dupuis added an empty-net goal in the final second.
Pittsburgh's 11 straight wins equals the longest such streak in the NHL this season. The Penguins are the first team in league history to win at least 10 in a row during three straight years.
Kunitz has moved within two goals of Tampa Bay's Steven Stamkos for the league lead in that department.