Heatley has 45 goals this season. Joseph Corvo, Daniel Alfredsson, Christoph Schubert, Patrick Eaves and Dean McAmmond also scored for Ottawa, which has earned at least a point in 20 of 21 games (15-1-5) since Feb. 8.
Corvo and Schubert also had two assists.
Dan Boyle had two goals for the Lightning, and Vincent Lecavalier added two assists to become the first Tampa Bay player to reach 100 points in a season.
Corvo put the Senators ahead 1-0 from the blue line at 2:38 of the first. The shot appeared to deflect off Tampa Bay centre Eric Perrin's stick.
Boyle tied it 1-1 with a power-play goal from the left circle with 5:03 left in the period.
Ottawa regained the lead just 53 seconds later when Alfredsson made a waist-high deflection of Heatley's pass in the low slot.
Boyle got the Lightning even again three minutes into the second. But Ottawa scored twice in a five-minute span after Tampa Bay goalie Marc Denis stopped Jason Spezza during a two-man breakaway midway through the second.
Heatley redirected Corvo's shot during a power play at 12:41 before the Senators took a 4-2 lead on Schubert's goal 1:26 later.
Ottawa's Ray Emery made a strong save on Tim Taylor's right circle shot shortly after Heatley's goal.
Eaves, McAmmond and Heatley all scored in the third period.
Notes: Lightning G Johan Holmqvist (flu) was scratched.