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7/5/2013 9:21 P.M. ET

Miami finding ways to win close games

ST. LOUIS -- Close games are starting to go the Marlins' way.

Donovan Solano's pinch-hit RBI single in the ninth inning on Thursday lifted the Marlins to a 4-3 comeback win over the Braves at Turner Field. A sign the team is maturing is its ability to pull out close games. Since May 31, the Marlins are 19-11. In that stretch, they are 6-2 in one-run games.

Early in the year, the Marlins were finding ways to lose when they went 14-41 in April and May.

Now, they are making up ground in their overall record in one-run games. For the year, they are 13-15.

The Marlins are getting contributions up and down the roster. On Thursday, it was Solano who came off the bench to deliver the big hit.

Not to be overlooked, reliever A.J. Ramos logged two shutout innings, striking out four, in Thursday's win. Giancarlo Stanton, who struggled at the plate on Thursday, going 0-for-5, made a run-saving catch to rob Dan Uggla in the ninth inning.

"I think that's kind of what happens when you start playing better and you get that good feeling and that confidence," manager Mike Redmond said. "Everybody wants to contribute. Everybody wants to get up with the game on the line."

The Marlins also are showing the ability to come back. They rallied to wins twice in Atlanta and have 17 comeback victories on the season.

"Maybe in the first couple of months, we weren't getting those hits," Redmond said. "But we knew they would come. It's fun to see guys contribute and be excited."

Dodgers, Giants make offers for Nolasco

ST. LOUIS -- At least two offers are on the table for Marlins right-hander Ricky Nolasco.

According to a league source familiar with the talks, the Dodgers are offering a pitching prospect and are also willing to assume the remaining nearly $5.7 million Nolasco will make this season.

The Giants are said to be the other club, offering two pitching prospects. But San Francisco is looking for Miami to assume at least a portion of what is left on the right-hander's contract.

The Marlins have had conversations with more than a half dozen teams regarding Nolasco. They may be waiting to see if any more tempting offers surface.

In the final year of a three-year, $26.5 million contract, Nolasco is eligible for free agency after the season.

The 30-year-old is 5-8 with a 3.85 ERA in 18 starts. He's logged 112 1/3 innings with 90 strikeouts and 25 walks.

Nolasco is Miami's all-time leader in wins (81), innings pitched (1,225 2/3), games started (197) and strikeouts (1,001). He's coming off an impressive victory in Atlanta on Wednesday, giving up two runs on six hits in seven innings. He struck out seven and became the first pitcher in franchise history to reach 1,000 strikeouts.

On Friday, Nolasco threw his scheduled between starts bullpen session, and he is scheduled to pitch for the Marlins on Monday against the Braves at Marlins Park.

Miami is expected to deal Nolasco by the July 31 non-waiver Trade Deadline.

While Nolasco is a likely candidate to be dealt, the Marlins have no intention of dealing slugger Giancarlo Stanton, who is eligible for arbitration in 2014. The 23-year-old won't have the necessary service time to become a free agent until after the 2016 season.

Miami has been receiving calls on relievers Steve Cishek and Mike Dunn. But neither is expected to be dealt. The two are arbitration eligible next year, and they are seen as core pieces for the future.

But reliever Ryan Webb, in his first season of arbitration, is a candidate to be traded. Miami has been in conversations with at least a couple of teams regarding Webb.

Marlins to make sure Stanton gets necessary rest

ST. LOUIS -- The way Giancarlo Stanton ran down Dan Uggla's long fly ball on Thursday night showed the right fielder legs are holding up. The Marlins are closely monitoring Stanton to make sure he stays that way.

Stanton missed all of May and the first week of June due to a strained right hamstring. His presence has been felt since returning on June 10. Miami is 14-8 with Stanton in the lineup since he returned.

The right fielder made the Marlins' most significant defensive play of the season in the ninth inning of Thursday's 4-3 win at Turner Field. With one out and a man on first, he sprinted into the gap and dove to rob Uggla of extra bases. If that ball had dropped, the Braves would have tied the score and had the winning run in scoring position.

Manager Mike Redmond keeps close tabs on Stanton's health. Right now, the 23-year-old wants to keep playing without periodic breathers. That could change on either Saturday or Sunday with back-to-back day games at St. Louis.

"Right now, we'll kind of going on how he feels and how he's moving around there," Redmond said. "I talk to him every day about how he's feeling. He says he feels great. He wants to play and he wants to be out there.

"You can kind of tell when a guy starts to drag a little bit out there, and give him some days. They have ways of letting you know they need a break."

Keeping Stanton out of the lineup is tough for Redmond, because he is one of the most feared sluggers in the game.

"Offensively, he's scuffling a little bit, but he will work through it," Redmond said. "He's one of those guys, his presence in the lineup, one swing and he's back on track."

Worth noting

• Miguel Olivo has cleared waivers, and he's elected to take free agency. The veteran catcher was placed on the restricted list by the Marlins on June 15 after he walked out on the team before a game the previous day. Olivo sought more playing time and asked for his release, and when that wasn't immediately granted on June 14, he packed up and left. The Marlins removed the catcher from the restricted list on Wednesday and designated him for assignment.

• Infielder Chris Valaika, recovering from a broken left wrist, is playing rehab-assignment games at Class A Jupiter. Top prospect Christian Yelich has been playing in rehab games at Jupiter since Wednesday. Yelich is on the Minor League DL with an abdominal strain. He went deep on Friday, marking his second straight game with a home run.

Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.