Zimmermann (9-3) allowed only two hits and a pair of walks while striking out eight in the 111-pitch gem.
Anthony Rendon provided an RBI single in the fourth, breaking a scoreless tie, and added a two-run double to cap a five-run outburst in the fifth inning.
Ian Desmond went 3-for-4 with a two-run single and three runs scored for the Nationals, who evened their three-game series in the opener of a day-night doubleheader.
Twins starter Scott Diamond (4-5) was tagged for seven runs (six earned) on 10 hits in a 4 2/3-inning effort.
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