Hanson (6-4) yielded two runs on six hits, didn't issue a walk and struck out six, rebounding from a poor outing Monday against St. Louis in which he lasted only 3 1/3 innings.
Eric O'Flaherty held Washington scoreless in the eighth despite issuing a pair of walks and Craig Kimbrel picked up his 16th save by striking out the side in the ninth as the Braves snapped a six-game losing streak to the Nationals.
Heyward followed by lining an 0-1 pitch into left field, putting Atlanta ahead.
Gonzalez lasted 4 2/3 innings, allowing three runs on seven hits.
Steve Lombardozzi knocked a solo homer for Washington, which came into the contest with a one-game lead in the National League East.
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