SAN FRANCISCO >> Once the Giants finally got a bunt down, the rest was easy.

A wild throw by reliever Randy Choate on a bunt allowed Brandon Crawford to score the winning run in the bottom of the 10th inning, lifting the San Francisco Giants over the St. Louis Cardinals 5-4 on Tuesday for a 2-1 lead in the NL Championship Series.

Crawford drew an eight-pitch walk from Choate to begin the inning, ending a stretch of 16 straight Giants retired since Tim Hudson’s two-out single in the fourth. After failing on two sacrifice attempts, Juan Perez singled to bring up Gregor Blanco.

Blanco fouled off a bunt try, too, but then pushed one to the left side of the mound and the left-handed Choate’s sidearmed throw sailed past lunging second baseman Kolten Wong, who was covering first base.

“We don’t do anything easy,” Giants manager Bruce Bochy said. “We might have got a little lucky there with Perez when he couldn’t get a bunt down and he gets a base hit. But Blanco laid down a beauty. … I don’t know if that’s luck as much as great bunt, great speed to put pressure on them.”

Randal Grichuk tied it with a solo homer in the seventh that chased Hudson.

Game 4 in the best-of-seven series is Wednesday night, with Ryan Vogelsong pitching for the Giants against fellow righty Shelby Miller.

This walkoff win came 12 years to the day after Kenny Lofton’s single in the ninth inning ended the 2002 NLCS against the Cardinals and sent the Giants to the World Series.

Playing without injured catcher Yadier Molina, the Cardinals had their chances. They squandered Wong’s double in the second before he delivered a wind-aided, two-run triple in the fourth.

Javier Lopez got the first two outs of the 10th before Jon Jay’s single, just the third hit by a left-handed batter against Lopez since he joined San Francisco in 2010. Two of those are by Jay this series.

Sergio Romo entered and retired Matt Holliday on a full-count grounder to third that Pablo Sandoval snared and fired to first.

Molina, nursing a strained left oblique sustained in Game 2 Sunday, began warming up Trevor Rosenthal in the bullpen in the ninth but never played.

A.J. Pierzynski went hitless in four at-bats starting in Molina’s place for St. Louis’ first postseason games back at AT&T Park since losing Games 6 and 7 of the 2012 NLCS, which it had led 3-1. San Francisco went on to capture its second World Series title in three years.

Journeyman Travis Ishikawa hit a three-run double in the first to stake Hudson to a 4-0 lead in his first postseason start beyond the division series in a 16-year career.

Hudson struck out five in 6 1-3 innings before giving way to Jeremy Affeldt.

St. Louis, last in the NL with 105 home runs during the regular season, has 12 in seven playoff games — eight in the seventh inning or later. The Cardinals connected in the seventh, eighth and ninth in Sunday’s 5-4 win.

Hunter Pence’s RBI double off John Lackey got things started in the first, the first time the Giants scored in the initial inning this postseason. Buster Posey and Sandoval hit consecutive two-out singles and Ishikawa followed an intentional walk to Brandon Belt to load the bases with his double.

The four runs were the Giants’ most in the first inning in the postseason since scoring six against Joe Wood of the Red Sox in Game 7 of eight in the 1912 World Series.

Wong had a fourth-inning triple aided by a blustery wind and a tricky bounce off the wall in right field.

UP NEXT

Cardinals: Miller makes his second career postseason start and fifth appearance looking for his first decision. He faced the Giants twice in relief during the ’12 NLCS, losses in Games 2 and 6 at AT&T Park.

Giants: Vogelsong has a 1.19 postseason ERA, and the Giants have won all five of his starts. He started the Division Series clincher against the Nationals, allowing one run in 5 2-3 innings. That made him the only pitcher in MLB history to yield no more than one run in his first five postseason starts. Curt Schilling is the only pitcher to have a longer streak at any point in his career, going six straight postseason starts allowing one run or fewer from 1993-2001.

PLUNKED

Hudson hit Lackey with a pitch on his left elbow in the fifth, making Lackey the first pitcher to be hit by pitch in the postseason since Steve Carlton was plunked by Tommy John in the 1977 NLCS.

TRAINER’S ROOM

Molina said he would try to swing Wednesday, and told a few reporters he would receive a cortisone injection to play through the pain.

SCORING FIRST

San Francisco hadn’t scored during the first inning in the postseason since Sandoval’s home run against Verlander in Game 1 of the 2012 World Series.