The Cardinals won the seven-match series against the Mets 4-3, and now take on the Detroit Tigers in the best of seven World Series starting on Saturday in Detroit.
Scores were tied at 1-1 deep into the match before 24-year-old Molina stepped up to the plate with Cards teammate Scott Rolen already on first base.
Molina, whose two older brothers are also major league catchers, then smashed a home run over the left-field fence off reliever Aaron Heilman to score two runs and set up the win.
"I was just trying to look for that pitch and put a good swing on it," Molina said.
The Mets rallied in the final inning and had the bases loaded with two outs, but St Louis closer Adam Wainwright struck out out-fielder Carlos Beltran to end the match.
"It was really in my opinion a classic game," St Louis manager Tony La Russa told reporters.
The Mets took an early lead with a run in the first inning through third baseman David Wright's single to right-field to score Beltran.
The Cardinals hit back straight away when a Ronnie Belliard bunt allowed Jim Edmonds to get home to even the scores in the second inning.
In the top of the sixth, Rolen looked to have broken the deadlock as he sent a line-drive way back, only to see Mets left-fielder Endy Chavez leap high above a 2.5 metre wall to take a great catch.
But the Cards would get their home run and win the match through Puerto Rican Molina, giving them a chance to avenge their World Series loss against the Boston Red Sox in 2004.
The Cardinals and the Tigers have met in the World Series twice before, with St Louis winning in 1934 while Detroit took the title in 1968, with both series going to seven games.