Latos (1-1), who lost in his major league debut July 18, allowed two runs and five hits over 5 2-3 innings. He walked two and struck out five.
Cristian Guzman and Ryan Zimmerman homered for the Nationals, who have lost 13 of 16 and have the majors' worst record at 28-68. Washington committed four errors for the third time this season.
San Diego took advantage of a passed ball, and an error by Washington starter Garrett Mock for two unearned runs in the first.
Tony Gwynn drew a leadoff walk, advanced to second on a passed ball and reached third when Mock (0-4) double-clutched on Everth Cabrera's sacrifice attempt for an error. Adrian Gonzalez hit a sacrifice fly then Cabrera stole second and scored on Chase Headley's two-out double to right to make it 2-0.
Guzman homered in the bottom of the first.
Rodriguez's solo shot made it 3-1 in the fourth. It was the second homer of the season and first since April 17 for Rodriguez, who increased his batting average from .194 to .203 with the 2-for-4 effort.
In the sixth, San Diego loaded the bases on three singles before Rodriguez hit a one-out, two-run single to right-center for a 5-1 lead, knocking Mock from the game.
Mock, making his second start since being recalled from Triple-A Syracuse on July 16, yielded five runs
- three earned - on nine hits. He walked one and struck out five.