Greening batted the puck out of the air after Patrick Wiercioch's initial shot was stopped by Ben Scrivens in the final minute, enabling the Senators to post a fourth straight win.
The Toronto center also provided two assists.
Mika Zibanejad and Erik Condra each tallied and added an assist for the Sens.
Ben Bishop -- subbing for the injured Craig Anderson -- earned the victory with 26 saves.
Scrivens finished with 32 stops for the Maple Leafs.