Gonzalez, who allowed 12 runs in his previous nine innings, retired the first 11 Reds batters before Joey Votto homered with two outs in the fourth. He struck out seven and walked two.
By the time Votto homered, Gonzalez (2-1) had a 6-0 lead.
Washington had lost nine of 12 and their previous six home games. Cincinnati has lost six of its seven road games.
The Nationals scored two runs in the bottom of the second against Bronson Arroyo (2-2). With one out, Ian Desmond singled. He scored on Espinosa's double. Kurt Suzuki singled. Gonzalez moved Suzuki to second with a bunt, and Espinosa scored on an infield single by Span.
Washington took a 6-0 lead in the third. Bryce Harper led off with his eighth home run of the year, the most any National has hit in April. Harper also doubled. He has 11 multi-hit games in the 22 Washington has played.
Following Harper's home run, Jayson Werth singled. Adam LaRoche, who had struck out six consecutive times, reached on a two-base throwing error by Votto at first. Werth scored on an infield out by Desmond. Espinosa hit his second home run of the year, a two-run shot, and Washington led by six.
Arroyo allowed six runs -- five earned -- in six innings. He walked one and struck out two.
Span's two-run triple in the eighth made it 8-1. Votto's home run was his fourth of the year.
NOTES: Reds OF Shin-Soo Choo walked in the ninth and has now reached base safely in his first 22 games this season. ... Nationals OF Roger Bernadina singled in the eighth inning. He had been 0 for 16. ... Washington C Wilson Ramos, who's on the 15-day disabled list with a strained left hamstring, will likely go on a rehab assignment this weekend when Double-A Harrisburg plays at Bowie. ... Espinosa celebrated his 26th birthday. ... Cincinnati LHP Sean Marshall, on the DL since April 10 with shoulder tendinitis, made his second rehab appearance Wednesday night for Triple A Louisville, pitching a scoreless inning against Gwinnett. He's been eligible to come off the disabled list since Tuesday and joined the Reds Thursday in Washington. "He's close. He's real close. He said he's feeling good," Reds manager Dusty Baker said. ... Cincinnati RHP Homer Bailey (1-1, 3.24) faces Washington RHP Jordan Zimmermann (3-1, 2.67) on Friday night.