Werth stroked a two-run double in the third inning, triggering a five-run outburst, and added a two-run single in the next frame as the Nationals took the opener of a four-game series.
Harper, returning to the line-up for the first time in more than a month due to bursitis in his left knee, blasted a homer in the first inning.
Ryan Zimmerman hit a pair of runs-scoring singles for Washington, which banged out 13 hits.
Jordan Zimmermann (12-3) notched his fourth win in five starts, yielding four runs on nine hits over six innings.
Brewers starter Yovani Gallardo (6-8) was torched for eight runs on nine hits in three frames.