Freese homered in the second inning off rookie Gerrit Cole and Adams connected in the eighth against reliever Mark Melancon to make it 5-1. Pete Kozma added an RBI infield single, and Wainwright finished it off by striking out Pedro Alvarez with two runners on base.
Alvarez became the first player to get an RBI in each of his first six postseason games, with a fluke hit that rebounded off first base in the seventh. But the Pirates were held to one run in each of the final two games in their first playoff series in 21 years. They haven't won a postseason series since the 1979 World Series.
"We were able to take a huge step forward this year in restoring the pride and the passion of the Pittsburgh Pirates' organization," manager Clint Hurdle said, "and rebonding our city with a ball team."
Cole beat the Cardinals with an impressive effort in Game 2, but they got to him early this time.
Freese made him pay for a full-count walk to Jon Jay with two outs in the second, lining a pitch into the visitors' bullpen beyond left field.
The Pirates had relief pitchers warming up in the fourth after Yadier Molina's infield hit and a throwing error put runners on second and third. Cole gave up just three hits over five innings, but was taken out of the game in the sixth.
Freese struggled this season to overcome a back injury in spring training and had nine homers and 60 RBIs. But just like teammate Carlos Beltran, he's an October star with seven homers, 29 RBIs and a .325 average in 36 career postseason games.
Adams, whose power hitting helped the Cardinals overcame an injury to power hitter Allen Craig in early September, hammered a first-pitch fastball from Melancon well over the right-field wall for his first RBIs of the series.
The Pirates scratched out their lone run on two infield hits and the single by Alvarez that looked to be a harmless inning-ending groundout before it hit the bag.