The catcher struck in the 10th to cap a fine individual performance, as the Phillies drew first blood at Minute Maid Park, having trailing by five at the end of the third.
Realmuto had already been a standout for the Phillies, with a two-run double in the fifth to level things up.
But his 346-foot line-drive home run was the sort of moment the 31-year-old had been dreaming of since he was a child.
"[I'm] just ecstatic to put a good swing on that pitch, be able to give our team the lead," he said. "We did such a good job fighting back there.
"I mean, ball games in the backyard, the whole 3-2, bases-loaded, two-out situation - I probably had 7,000 at-bats in that situation growing up."
Realmuto is the first catcher to score an extra-inning home run in the World Series since Carlton Fisk achieved the feat in 1975.
Nick Castellanos says the Astros will not dwell on their first loss of the postseason.
"Let's go to work," he said. "We've been there before. I think that's what this team does so well.
"We know there's no quit, really. We really respect all 27 outs, and we take that seriously, and we take it [pretty] personal."