Each team used all its relievers.
Medlen, scheduled to start Tuesday at the Mets, made his first relief appearance of the season as Atlanta's ninth pitcher of the night.
Soriano suffered his sixth blown save. Heyward's second homer of the game, a two-run shot to right-center with two outs in the ninth, sent the game to extra innings.
Braves pitchers hit Bryce Harper with two pitches in Atlanta's win on Friday night, leaving the outfielder bruised and unable to start on Saturday night.
That set the stage for Strasburg.
Strasburg hit Upton in the first inning one pitch after Heyward's leadoff home run. The pitch hit Upton's backside, and he quickly ran to first.
Asked if he meant to hit Upton, Strasburg said "I'm not going to get into that."
But the answer seemed clear.
"Well after somebody goes deep and you hit him in the rear end, I don't think it's a big deal," Johnson said. "I don't know if he did it on purpose or not."
The second-inning meltdown by Strasburg was more difficult to figure out.
The drama left Braves fans howling, but no players emerged from either dugout. There were no additional incidents in the game.
There were tensions between the teams that carried over from the Braves' three-game sweep at Washington on Aug. 5-7. Both benches emptied when Harper was hit by a Julio Teheran pitch in the second game of the series.
Tanner Roark dominated the Braves after taking over for Strasburg. Roark allowed only one hit in four scoreless innings. He had a run-scoring double in the fifth for his first major league hit and RBI.
Mike Minor allowed four runs in only 1 2-3 innings, the shortest of his 78 career starts.
Minor gave up bases-loaded, two-run singles to Wilson Ramos in the first and Jayson Werth in the second.
Harper was in Johnson's original lineup, but was held out with bruised triceps until entering the game as a defensive replacement in the ninth.
Strasburg gave up two runs and two hits, two walks and one hit batter in one-plus inning. Like Minor, he also had the shortest start of his career.
Werth doubled off Luis Ayala in the sixth and scored on a single by Wilson Ramos.
NOTES: Washington's Scott Hairston was ejected by Hudson in the ninth for arguing a called third strike. ... The Nationals placed RHP Taylor Jordan on the 15-day DL with a lower back strain. Tyler Moore was recalled from Triple-A Syracuse and had two hits while starting at first base. ... The Braves signed IF Tyler Greene to a minor league contract. Greene, released by the Chicago White Sox on Tuesday, was assigned to Triple-A Gwinnett. ... 2B Dan Uggla, who had corrective eye surgery on Friday, said a test Saturday showed his vision at 20-15. He expects to be ready to play when eligible to come off the 15-day DL on Aug. 28. ... The series concludes on Sunday when Nationals LHP Gio Gonzalez faces Atlanta's Julio Teheran.