The Cubs ended a 108-year wait for the World Series with victory over Cleveland last November.
Chicago, who ended a 108-year wait for the World Series with victory over Cleveland last November, slipped to defeat after Grichuk's decisive play in the bottom of the ninth inning.
The Cardinals engineered a game-winning position after Jose Martinez lined up a double in right-center off Mike Montgomery.
Yadier Molina was then walked intentionally before Kolten Wong worked another walk, allowing Grichuk the chance for his walk-off hit.
Elsewhere Sunday, San Francisco Giants pitcher Madison Bumgarner clubbed two home runs but it was not enough to stop the Arizona Diamondbacks snatching a 6-5 win.
Bumgarner became the first pitcher in Major League Baseball history to hit two homers on Opening Day and looked to have helped the Giants into a game-winning position as they led 5-4 in the ninth.
But Arizona shortstop Chris Owings singled home the winning run with two outs in a two-run ninth inning to give the D-Backs victory at Chase Field.
Earlier, Bumgarner hit bases-empty home runs in the fifth and seventh innings to put the Giants 4-3 ahead. On the mound, Bumgarner struck out 11 and gave up six hits and three runs.
Arizona tied the game in the eighth inning after consecutive singles by A.J. Pollock, Owings and Paul Goldschmidt off Derek Law.
Bumgarner's double blast on Sunday took his career home run tally to 16.
He joined Barry Bonds (2002), Matt Williams (1994) and Willie Mays (1964) as the only Giants to score two home runs on Opening Day in the past 50 years.
In Florida, the Tampa Bay Rays thumped the New York Yankees 7-3 at Tropicana Field with Japanese pitcher Masahiro Tanaka having a nightmare start to the season.
Tanaka gave up seven runs from eight hits and was removed after less than three innings.
It was the worst Opening Day performance by a Yankees pitcher in history.
"That was puzzling for us -- there are going to be days where you don't have great stuff, but usually because of his command, he can find a way to get through it," Yankees manager Joe Girardi said. "Today, he didn't have his command either. It's hard to figure out."
Evan Longoria and Logan Morrison both homered and drove in three runs for the Rays, who had never managed to beat Tanaka before in eight previous attempts.
Tanaka was hooked after 67 pitches, with reliever Tommy Layne coming in for the final out of the third inning.