Hyun-Jin Ryu starred for the side as he did not allow a hit until the fifth inning as the Dodgers cut the deficit to 2-1 in this best-of-seven series.
St Louis had an excellent chance to put one foot in the World Series with another victory, but they failed to capitalise on an equally impressive performance from their pitcher Adam Wainwright, who gave up just six hits and two runs in seven innings.
The Cardinals managed just four singles, but their woes were summed up by the fact they could not get a runner to third base as their offence once again flattered to deceive.
Adrian Gonzalez and Yasiel Puig drove in runs in the fourth inning to put the Dodgers on top, with the former's hit ending Los Angeles' scoreless innings streak at 22.
Victory was ensured in the eighth inning when Hanley Ramirez, playing with a fractured rib, scored Carl Crawford with a single.