It was Ottawa's first loss of the season and came despite a four-goal outburst in the second period that briefly gave the Senators a 4-2 lead. Tampa Bay improved to 3-1.
Malone tied it at 4-4 3:39 into the final period and gave the Lightning the lead with 7:02 to play. Tom Pyatt added an empty-net goal with 42 seconds to play.
Erik Condra, Jason Spezza, Erik Karlsson and Kyle Turris all scored for Ottawa during the second period in the Senators' bid to open the season with four straight wins. Their loss left New Jersey, Chicago and San Jose as the only teams in the league without a setback.
Anders Lindback made 32 saves for the Lightning. Ottawa's Ben Bishop stopped 25-of-30 shots.