With the score tied 2-2 entering the bottom of the sixth, the Nationals loaded the bases with none out against Kyle Weiland (0-2) and, after Travis Buck struck out, Lombardozzi blooped a double to left, scoring two runs.
Lombardozzi finished 4-for-5 for the Nats, who won for the sixth time in seven games and improved to 8-3.
Stephen Strasburg (2-0) limited the Astros to two runs on six hits over six innings, issuing only one walk while striking out five.
Henry Rodriguez earned his second save of the season with a scoreless ninth.
Weiland was tagged for six runs on 10 hits in a 5 2/3-inning effort for Houston.
Chris Johnson went 2-for-4 with a pair of RBI for the Astros.