The Senators completed a four-game season sweep of the Panthers and moved into a tie with Florida for the bottom two spots in the Eastern Conference at 70 points.
Nick Foligno gave Ottawa the lead with the only goal of the first period and the rest of the scoring all took place in the second.
Greening gave the Senators a 2-0 advantage 2:30 into the middle period and then tallied 4 minutes later to put Ottawa in front 3-1. Defenseman Filip Kuba produced the other Ottawa goal, his first of the season in 60 games.
Florida lost its seventh in a row. Scott Clemmensen took the loss, giving up four goals on 23 shots.