The Cardinals broke open a scoreless game in the third inning when Daniel Descalso led off with a single against Dodgers starter Ricky Nolasco, moved to second on a sacrifice and scored on Matt Carpenter's RBI double.
Holliday (2-for-4) then followed by blasting a pitch 403 feet to left field for a 3-0 advantage.
Lance Lynn (2-0) earned his second NLCS win, allowing two runs on six hits over 5 1/3 innings. He walked three and struck out five.
Seth Maness and Carlos Martinez combined for 2 2/3 scoreless relief innings and Trevor Rosenthal closed out the victory with his second save.
The Cardinals will attempt to earn a World Series berth with another win in Wednesday's Game 5 at Los Angeles.
Nolasco (0-1) ended up surrendering three runs on three hits over four innings.
Yasiel Puig went 2-for-3 with an RBI for the Dodgers.