George Springer smashed a two-run homer in the top of the 11th to cap the Astros' late charge.
It proved just enough as the teams combined for an astonishing five extra-inning home runs -- a record for a Major League Baseball post-season game.
"That's an incredible game on so many levels, so many ranges of emotion," said Astros manager A.J. Hinch. "That's one of the most incredible games you'll ever be a part of."
With the win the Astros head home on level terms for games three four and five on Friday, Saturday and Sunday.
Marwin Gonzalez homered for the Astros in the ninth to tie it at 3-3 after the Dodgers had seemingly been heading for victory.
Jose Altuve and Carlos Correa ripped back-to-back homers in the top of the 10th to put Houston up 5-3.
Undaunted, the Dodgers responded in the bottom of the 10th with a lead-off homer from Yasiel Puig.
With two outs in the 10th, Astros relief pitcher Ken Giles walked Logan Forsythe, who reached second on a passed ball and raced home when Enrique Hernandez belted a single to right field.
With the score at 5-5, Dodgers relief pitcher Brandon McCarthy surrendered a single to Cameron Maybin to open the 11th.
Springer followed to put the Astros ahead for good -- although the Dodgers pulled within 7-6 with Charlie Culberson's homer in the bottom of the 11th.
"It was an exciting baseball game," Dodgers manager Dave Roberts said. "It was an emotional roller-coaster."
Astros ace pitcher Justin Verlander pitched four-plus innings of no-hit ball.
But the two hits he surrendered in six innings were home runs to Corey Seager and Joc Pederson that gave the Dodgers the early advantage.
Pederson rewarded Dodgers manager Dave Roberts's faith with a game-tying homer to right field with two outs in the fifth.
Pederson, picked to start in left field over Andre Ethier because Roberts said he liked Pederson better against Verlander's velocity, connected on an 88 mph (141.62 Km/h) slider to level the score at 1-1.
Seager made it 3-1 in the sixth with a two-out home run to left field off Verlander that also scored Chris Taylor, who had walked.
Houston had opened the scoring in the third inning, when Josh Reddick singled off of Dodgers starter Rich Hill and advanced to second on Verlander's sacrifice.
A single from Springer put runners on the corners. Alex Bregman followed with a sharply hit single to center field, where the ball eluded diving Dodgers center fielder Taylor, knocking the brim of his cap.
Reddick scored, but the ball bounced toward Pederson, who corralled it to hold Springer and Bregman on base. Hill then struck out Jose Altuve and Carlos Correa to end the inning.
source: news.abs-cbn.com
