La Roche went 2-for-four and drove in three runs to back up Gio Gonzalez (10-4), who gave up five runs – four earned -- on eight hits in six innings.
Tyler Moor contributed a three-run homer for the Nationals and Ryan Zimmerman had three hits, including a solo homer.
Dexter Fowler and Jonathan Herrera hit solo home runs for Colorado. The Rockies are 4-15 since June 5.
Christian Friedrich (4-5) allowed four runs on nine hits over 4 1/3 innings before turning the ball over to Guillermo Moscoso, who was lit up for eight runs in 1 2/3 innings, five of them in the fifth.