Leo Nunez (2-3) took over in the eighth with Florida ahead 5-3. Rick Ankiel led off with a single, Albert Pujols walked on a full count and Ryan Ludwick singled. The ball got under Ross' glove and went to the wall, letting Ankiel and Pujols score the tying runs.
"I missed it, flat out," Ross said. "Trying to block it and it just went right through my legs. The game is on the line right there and I got to come up with that play. There's no excuse."
Rasmus batted for Trever Miller and singled to right.
"You just want to make contact," said Rasmus, who extended his career-high hit streak to 10 games. "It's not like you're changing your thought process. You just want to have a good at-bat."
Pujols hit his 19th home run and Ankiel added three hits for the Cardinals.
"Our production was pretty good again today," Ankiel said. "I feel we're headed in the right direction and now we can head back home and hopefully keep it going."
Ross Gload homered twice for the Marlins. He drove in three runs with the first multihomer game of his career.
"It didn't help us win the ballgame," Gload said. "It wasn't enough."
Miller (2-0) pitched a scoreless seventh. Ryan Franklin recorded his 14th save by going 1 2/3 innings.
Pujols reached into the first-base stands and caught Wes Helms' foul popup with a runner on second for the final out. The Marlins finished 6-5 on their homestand.
"The homestand is a success because you have a winning record at home, but games like this, you want to win those games," Marlins manager Fredi Gonzalez said.
Gload put the Marlins ahead with a two-run homer in the second off Todd Wellemeyer.
Miller was cruising along, having retiring 14 straight batters, until Ankiel singled in the sixth. Pujols followed with a two-run homer off the left-field foul pole.
"That wasn't a situation where I was going to nibble on [Pujols] at 3-1," Miller said. "He's too good of a hitter, he's not going to chase a bad pitch. He's going to get his pitch and hit it. Unfortunately, he did."
Gload responded in the bottom half, leading off with a home run to right. He went into the game with only one home run this season.
Wellemeyer allowed five runs and 11 hits in six innings. Miller gave up three runs and seven hits in 6 1/3 innings, striking out eight without a walk.
"We didn't make some adjustments against Miller, but we kept at it and came through," Cardinals manager Tony La Russa said. "He was pretty tough on us, but then we found a way."
Ankiel went 8-for-13 with four extra-base hits in the three-game series after hitting .152 in his previous 15 games. ... The Cardinals scored 19 runs in the last two games after scoring 15 runs in the previous six games. ... Marlins catcher John Baker is hoping to return to the lineup on Friday after being struck on a backswing in Tuesday's game, causing him to receive six stitches. ... Marlins right-hander Anibal Sanchez is not expected to come off the DL when he is eligible on June 18.