The Marlins were trailing 1-0 in the ninth but forced extra innings when Giancarlo Stanton blasted a 425-foot solo homer off Nationals closer Rafael Soriano.
Leading off the 10th, Hechavarria sent a grounder to third baseman Chad Tracy, who threw wildly to first, allowing Hechavarria to reach second.
That brought up Lucas, who sent a slow grounder to second baseman Steve Lombardozzi. Ruggiano was out at second, but Lucas beat out the relay to first on the double-play attempt, allowing Hechavarria to cross home with the winning run.
Steve Cishek (3-4) earned the victory as Miami clinched its three-game series.
Jayson Werth drove in the only run for Washington, which fell to 1-5 on its seven-game road trip.