It was a dramatic Game 2 as the teams combined to score nine of the 13 total runs from the eighth inning on, and seven of those in extra innings. Six home runs were hit from the ninth inning on, with five coming in extra innings.
The Dodgers' Charlie Culberson made it close with a home run in the bottom of the 11th, but Astros right-hander Chris Devenski (1-0) struck out Yasiel Puig to end it.
Springer's home run in the 11th off Dodgers right-hander Brandon McCarthy (0-1) came after both teams scored twice in the 10th inning.
The Astros took the lead in the 10th on home runs from Jose Altuve and Carlos Correa, but the Dodgers tied it a half-inning later on a home run from Puig and a two-out RBI single from Enrique Hernandez.
The series now shifts to Houston on Friday for the first of three games.
The victory was the Astros' first in the World Series in six tries. They were swept in 2005 by the Chicago White Sox and lost Game 1 to the Dodgers 3-1 on Tuesday.
Trailing by two runs in the eighth inning, the Astros started their comeback against the dependable Dodgers bullpen. Alex Bregman hit a leadoff double against Brandon Morrow. One out later, Correa delivered an RBI single off Los Angeles closer Kenley Jansen to get Houston within a run.
Marwin Gonzalez homered off Jansen leading off the ninth to tie it 3-3.
In the 10th, Altuve and Correa both went deep against Dodgers right-hander Josh Fields, who failed to record an out. The Dodgers scored their two runs in the 10th off Astros closer Ken Giles.
Coreg Seager gave Dodgers a 3-1 lead when he hit a two-run home run in the sixth inning off Astros starter Justin Verlander. It was one of two hits Verlander allowed over six innings, but both were home runs.
Dodgers starter Rich Hill went only four innings, throwing 60 pitches in the process. He gave up run on three third-inning hits while striking out seven. Former starter Kenta Maeda followed Hill with 1 1/3 scoreless innings.
The Dodgers then went to left-hander Tony Watson and right-hander Ross Stripling (one batter each) before Morrow handed it off to Jansen, who had converted his first 12 career playoff save chances before blowing the save Wednesday.
Correa's RBI single off Jansen ended the Dodgers' playoff record 28 consecutive postseason innings without giving up a run.
Joc Pederson, a surprise starter in left field for the Dodgers, not only tied the game with one swing in the fifth inning, but also delivered the first hit off Verlander. Pederson had played only four games in left field this season and six games there in his entire four-year career.
The Astros took a 1-0 lead in the opening inning on an RBI single from Bregman.
Of the previous 58 times the World Series was tied 1-1, the winner of Game 2 captured the title on 30 occasions (51.7 percent).
NOTES: Before Game 2, Astros 2B Jose Altuve was named the AL's winner of the Hank Aaron Award as the most outstanding offensive player in his league. The NL Hank Aaron Award went to Marlins OF Giancarlo Stanton. ... Astros manager A.J. HInch named his starters into the weekend, saying RHP Lance McCullers would get the ball in Game 3 and RHP Charlie Morton would start in Game 4. ... The Dodgers have already lined up their rotation for Houston, with RHP Yu Darvish pitching in Game 3 and LHP Alex Wood getting the ball in Game 4. ... Dodgers OF Joc Pederson has two postseason home runs, his game-tying shot in Game 2 on Wednesday and one in the Dodgers' Game 5 clincher of the NL Division Series last season at Washington.