Espinoza, who socked a go-ahead, three-run homer in the first game, stroked an opposite-field hit into the left-field corner, chasing home Ian Desmond, Jerry Hairston Jr. and Matt Stairs to break a 1-1 tie.
Hairston went 3-for-4 with a solo homer and Adam LaRoche also went deep for the Nationals, who beat the Brewers 8-4 in the opener.
Livan Hernandez (2-1) held Milwaukee to six hits, walking none and fanning three. Drew Storen picked up his first save of the year with two innings of scoreless relief.
The Brewers' Kameron Loe (1-1) absorbed the loss after surrendering the hit to Espinoza.