ST. LOUIS -- Every run Sunday came via a solo homer.
After homering to lead off the top of the fourth, giving him 30 in a season for the first time in his career, Morrison rifled a 1-1 fastball from Sam Tuivailala 411 feet to the bleachers in right-center.
"It started with LoMo and it ended with LoMo," Rays manager Kevin Cash said.
It tends to start with Morrison when Tampa Bay (65-67) leaves Florida's Gulf Coast. Twenty-two of his homers this year have occurred on the road, including 11 of the last 13.
Tuivailala (3-3) said he threw a bad pitch and paid the price.
"We had a game plan and I was trying to follow it, but I made a mistake and left the pitch out over the plate," he said. "He did the damage."
It allowed the Rays to start a potentially season-defining nine-game road trip with a series win, although it gained them no ground in the American League wild-card standings. They remain three games behind Minnesota for the AL's second wild-card spot.
Meanwhile, St. Louis (65-65) stayed 4 1/2 games behind the Chicago Cubs for first place in the National League Central. It was the third time in four days the Cardinals have lost when Chicago has lost, and the sixth time this month they've lost on the same day as a Cubs defeat.
"We just couldn't finish like we needed to," St. Louis manager Mike Matheny said.
Pitching ruled most of the day. Tampa Bay's Chris Archer and the Cardinals' Lance Lynn each turned in quality efforts, giving up runs only when the bases were empty.
Archer permitted just five hits and a run in seven innings, walking one and fanning eight. While his streak of three straight starts with 10 or more strikeouts ended, Archer carved up the St. Louis lineup with a three-pitch mix.
One of them was a changeup, a pitch Archer has showcased more at the insistence of teammate Steven Souza Jr. In an interesting turn of events, Souza actually crashed Archer's post-game interview to query him about the new pitch.
"I'm starting to trust it more, especially against left-handed hitters, and I'm sprinkling it in against righties," Archer said. "He (Souza) has seen it, and he's been telling me to use it."
Until Kolten Wong rocked a one-out solo homer in the seventh, St. Louis got just one runner to scoring position. Greg Garcia doubled in the third and reached third on Lynn's groundout, but Matt Carpenter bounced out to first.
A later Carpenter at-bat proved a bit more fruitful. He touched Dan Jennings for a game-tying leadoff homer in the eighth, his 17th. It was his first bomb off a lefty since clouting a walk-off grand slam April 27 against Toronto's J.P. Howell.
The Cardinals got runners to the corners later in the inning on a Yadier Molina single that moved Paul DeJong to third. But Wong grounded out to second.
Brad Miller accounted for the Rays' other run with a leadoff homer in the seventh that barely cleared the center-field wall and the leaping Dexter Fowler. It was Miller's sixth homer, one year after jacking a career-high 30.
Lynn worked seven innings, giving up six hits and two runs with three walks and eight strikeouts. It was his 10th straight game of at least six innings.
But it wasn't enough to keep St. Louis from falling to 4-9 since tying the Cubs for first place two weeks ago. Morrison made sure of it on a day where he reached a milestone.
"Having never done it before, 30 is a pretty special club," Morrison said. "Hopefully, I can keep swinging it and get into an even more special club."
NOTES: St. Louis 3B Jedd Gyorko (right hamstring strain) was placed on the 10-day DL Sunday after injuring himself in the eighth inning Saturday night. The club recalled 1B Luke Voit from Triple-A Memphis. ... Prior to Sunday, Tampa Bay had lost six consecutive games when hitting at least three homers. ... Cardinals CF Dexter Fowler (illness) was back in the lineup Sunday, batting fourth. Fowler was sent home Saturday night as a precaution in case he was actually contagious.