Dexter Fowler -- who singled behind Wilin Rosario's double for a third-inning run -- tripled off Strasburg to open the sixth, then Strasburg uncorked a 95 mph pitch that hit Scutaro in the batting helmet.
Scutaro was able to stand, but Rockies head athletic trainer Keith Dugger didn't let him continue, and Chris Nelson replaced him. Scutaro was able to walk to the dugout. A club official reported that Scutaro said he was "fine" after the game, and his status is listed as day-to-day.
Carlos Gonzalez followed Scutaro's beaning with a single to tie the game at 2-2. Michael Cuddyer singled to load the bases, and Todd Helton's sacrifice fly put the Rockies ahead to stay.
The inning marred what looked like a big evening for Strasburg (9-2), who struck out eight, but gave up three runs on six hits for the National League East-leading Nationals (41-30).
Helton said he did not believe Strasburg's struggle in the sixth and his accidental plunking of Scutaro were connected.
"I don't know if that played too much into it, but it gave us an extra base runner," Helton said. "Carlos had a great at-bat, Cuddy had a great at-bat and it gave me the luxury of hitting a pop fly to get a runner in."
Strasburg escaped the inning without any further damage.
"It happens, part of baseball," Strasburg said. "You try to get in and obviously you never want to hit a guy in the head, but you have to keep going out there and pounding the strike zone. You think about it for a second, and hope he's OK. Once I saw him walk off, I figured he'd be OK."
After the shaky sixth, Nationals manager Davey Johnson replaced Strasburg with Tom Gorzelanny.
The victory in the opener of a seven-game homestand ended an uncharacteristic home losing streak for the Rockies (28-44) at six games. They came up empty in their last homestand, an Interleague date with the Angels and Athletics June 8-14.
"It's always nice to get a win here at home," Fowler said. "We're a dominant team at home and it was obviously disappointing the last time we were here."
Nelson, who turned his right ankle on Saturday and did not play on Sunday, singled home Eric Young, who drew a walk from Gorzelanny to open the seventh, making it 4-2.
Rockies starter Jeff Francis, mixing an 86 mph fastball with curveballs that floated in at 68 mph, held the Nationals to five hits and two runs in five innings. Francis' five strikeouts included two by Nationals young power hitter Bryce Harper in his Coors Field debut.
With the Rockies working with a four-man rotation and 75-pitch limit, manager Jim Tracy removed Francis with the Rockies trailing, 2-1. It was not the best position when facing Strasburg.
"Impressive," Francis said. "I left the game and we were losing. There are probably a lot of days in this summer when that game ends 2-1. We did a great job of coming back and scoring some runs on him."
Francis has become the poster child for the unusual pitching plan. In his last two starts, he has given up three runs in 10 innings, struck out eight and hasn't walked anyone. He also has ended up with a pair of no-decisions, but the Rockies have won both games.
It's certainly a change. Francis threw 215 2/3 regular-season innings and 16 2/3 in the postseason in 2007, when the Rockies won the NL title and bowed to the Red Sox in the World Series. But he is not fighting the strategy.
"It's different, for sure," Francis said. "It's not what we're used to. But we're asked to do a job. That's what I was asked to do today. If we can do that, over the long haul, we're going to feel like we're going out there a lot more often."
Reliever Josh Roenicke (3-0), who entered leading Major League relievers with 42 1/3 innings pitched, gave up one hit, struck out two and walked one in two scoreless innings.
Matt Belisle threw a scoreless eighth with two strikeouts and Rafael Betancourt earned his 12th save in 15 attempts, despite allowing two baserunners with one out. It represented a good start after a 3-6 road trip.
"We did enough offensively to win, and pitching is what it boils down to," Rockies manager Jim Tracy said.