Strasburg went six innings to earn the win -- and a group hug in the dugout when he was done on the mound.
"They keep squeezing me a little harder every time," he said. "That's OK."
Kurt Suzuki hit a tiebreaking homer in what became a messy six-run seventh, and the Nationals headed back home needing two wins in three potential games in Washington to claim their first championship.
Adam Eaton paraded around the bases pointing to the Houston crowd after a late home run as the Nationals won their eighth in a row. They've won 18 of 20 overall dating back to the regular season, with the last two over AL Cy Young Award favorites Gerrit Cole and Verlander.
"Probably going to be a little frigid, might be a little cold, so bring your jackets and your beanies," said slugger Anthony Rendon, who hit a two-run double in the first inning.
The 31-year-old Strasburg had waited years for this chance. Back in 2012, he was about two years removed from Tommy John surgery when Nationals brass decided protecting his elbow was more important than pitching him in the playoffs, so he was shut down late in a season full of promise.
Making his Series debut, Strasburg allowed a two-run homer to Alex Bregman in the first before throwing five shutout innings to improve to 4-0 this postseason. He allowed seven hits and struck out seven.
Nationals manager Dave Martinez was asked what's made Strasburg so good this October.
"One, he has the confidence to do it and two, he's become a premier pitcher, a big-game pitcher," Martinez said. "He doesn't get rattled."
Verlander, so good in the regular season, fell to 0-5 in six World Series starts. He gave up seven hits and four runs, and was lifted after walking a batter following Suzuki's home run.
Verlander led the majors with 21 wins this season and struck out a career-high 300 to reach 3,000 in his career. He has a World Series ring, MVP and Cy Young Award trophies, and three no-hitters to his name.
He fanned six to become the career leader in postseason strikeouts with 202 -- another impressive statistic on a stellar resume that's still missing that elusive World Series win.
"Obviously it's magnified in the World Series when you're not clicking on all cylinders," Verlander said.
Their wins against Houston's best pitchers turned the underdog Nationals into heavy favorites to take the title.
Only three of the previous 25 teams to lose the first two games at home under the 2-3-2 format have come back to win the Series. No one has done it since the 1996 New York Yankees.
"I wish I was a betting man, but I'm not," Martinez said. "I don't really believe in that stuff. ... We're here because the boys never gave up."
Long after most players had left the field and only a handful of Nationals were left, a small but boisterous crowd of Washington fans assembled behind their dugout. The red-clad group cheered and waved their hands as players ascended the dugout stairs, finishing up an out-of-town party they hope to continue at home on Friday.
But the Astros insist the tough start hasn't dampened their confidence.
"We have a really good team," manager AJ Hinch said. "Clearly, the Nats have outplayed us -- bottom line. They came into our building and played two really good games. We're going to have to try to sleep off the latter third of this game."
Added shortstop Carlos Correa on digging out of the early hole: "If there is a team out there that can do it, it's us."
Things went wrong immediately for Verlander when he walked leadoff man Trea Turner on four pitches. Eaton, who homered in the eighth, singled before Rendon, the Houston native who said he'd certainly have 100 friends and family members at Minute Maid Park for each game, knocked a ball off the wall in left field to put the Nationals up 2-0.
"This is my city. I love Houston," Rendon said. "We were going to try to just steal one game and we just happened to steal two, and we've got to take care of business at home."
Verlander got his 200th postseason strikeout when he fanned Victor Robles in the second. The eight-time All-Star passed John Smoltz, who had 199 and was in the TV booth for Fox to see his record fall.
Verlander and Strasburg both settled in after early wobbles, until Houston fell apart in the seventh.
Suzuki sent Verlander's 100th pitch sailing above the seats in left field to start the inning. Ryan Pressly, who left Game 6 of the ALCS with a knee injury, took over and didn't look right from the start.
He walked Turner before Hinch called for his first intentional walk of the season when he gave Juan Soto a free pass to load the bases with two outs. Howie Kendrick, Asdrubal Cabrera and Ryan Zimmerman followed with successive singles to bust it open, putting the Nationals up 8-2. As those hits were piling up and run after run crossed the plate, many in the stunned sellout crowd of 43,357 began streaming for the exits.
Hinch was asked what happened in the seventh.
"Where would you like me to start?" he said.
Michael A. Taylor padded the lead further with a solo homer off Chris Devenski in the ninth.
The only time Strasburg was under any real duress after the first inning came when Yuli Gurriel doubled with one out in the sixth before the Nationals intentionally walked Yordan Alvarez. The slumping Correa hit a weak fly ball before rookie pinch-hitter Kyle Tucker struck out, allowing Strasburg to wriggle out of the jam and end his solid night.
Sanchez has made two sharp starts this postseason and took a no-hitter into the eighth inning in Game 1 of the NLCS against St. Louis.
Greinke, acquired from Arizona at the July 31 trade deadline, is 0-2 with a 6.43 ERA in three October outings.