Arenado led off the 13th with a double off the wall in left field against Sam Dyson (2-1). Dickerson followed with a liner to right, and Arenado easily beat the throw from Giancarlo Stanton.
It was the sixth walk-off win for the Rockies.
"We left a ton of guys on base. One-run games in this ballpark -- that's tough because you can put a big number up in one swing," Redmond said. "We had chances. We had lots of chances."
Adeiny Hechavarria gave the Marlins a 4-3 lead in the ninth with an RBI single off closer LaTroy Hawkins. Dickerson tied it in the bottom half with a 455-foot drive off Cishek for his 19th homer. It was Cishek's fourth blown save this season.
"I fell (behind) 3-1 to a guy that's an all-or-nothing hitter and when you miss down and in to a lefty that's a power hitter, it doesn't put you in a good spot or the team in a good spot," Cishek said. "Unfortunately, I left a good pitch to hit to a pure fastball hitter and he got all of it."
The Rockies erased a 1-0 deficit in the third inning with a run on a double play and a two-run homer by Brandon Barnes.
Miami got a run in the fourth when Jordan Lyles walked Donovan Solano with the bases loaded, and then tied it on Jarrod Saltalamacchia's RBI double in the fifth.
Lyles left after giving up a pair of two-out singles in the sixth, but lefty Rex Brothers struck out Garrett Jones to end the inning.
Lyles allowed three runs on seven hits, struck out five and walked five.
Miami starter Tom Koehler's only blemish was the third inning. He struck out four and didn't walk a batter in tossing seven solid innings.
After allowing two singles to lead off the fourth he retired 11 of the last 12 batters he faced. The one single he allowed was wiped out on a caught stealing.
Hechavarria saved a run in the bottom of the 12th when he raced out and made a leaping catch of Justin Morneau's blooper with two outs. Had the ball fallen Rockies pitcher and pinch runner Tyler Matzek would have scored from third.
"I don't how he got to that ball. At the time, it was a huge game-saving play," Redmond said. "It's too bad we couldn't come back and flip a run out there, but it wasn't our night."
The Marlins had a rally going in the 11th when the first two batters reached. But the inning turned strange when Marcell Ozuna's line drive went off the glove of shortstop Josh Rutledge. Rutledge got the ball and tagged second for one out and Casey McGehee was caught between second and third. He was tagged out in a rundown.
"I was just trying to get a ground ball out there and it ended up being a line drive," Rockies reliever Nick Masset said. "I was saying, `Tag the guy, no tag the base.' Just excited about the way it went."
Marlins: No injury updates.
The Marlins will send LHP Brad Hand (2-5, 4.52) against RHP Christian Bergman (0-2, 7.20) in the last game of the three-game set. Bergman is making his first start since breaking his left hand in a start against Milwaukee on June 20.