Price originally was slated to throw Saturday, but was pushed back to Sunday due to illness and thus opted out of Tuesday's All-Star Game in order to avoid pitching on just one day of rest.
Rodney drew the call from Red Sox manager John Farrell, giving the Mariners four All-Star representatives, as he joins Felix Hernandez, Robinson Cano and Kyle Seager to give Seattle its largest contingent since five Seattle players were chosen in 2003.
"When you see something happen like that, you have to understand what's going on," Rodney said of his late addition. "I knew I had maybe the numbers to be there. I'm happy to be there with that group of people."
The AL squad now includes six relievers, as Rodney joins Kansas City's Greg Holland (24 saves, 1.87 ERA), Minnesota's Glen Perkins (22 saves, 3.05 ERA), Oakland's Sean Doolittle (13 saves, 2.98 ERA), New York's Dellin Betances (one save, 1.46 ERA) and Boston's Koji Uehara (18 saves, 1.65 ERA), who was added to the team to take the place of injured Yankees starter Masahiro Tanaka.
Rodney also was an All-Star in 2012 with the Rays when he had 25 saves and a 0.93 ERA at the break on the way to a career-best 48-win, 0.60 ERA season when he was AL Comeback Player of the Year Award winner and finished fifth in the AL Cy Young Award voting.
That year, he accompanied Price as the Rays' representatives. This year, he's replacing his former teammate.
"He gave me a break," Rodney said. "I love him."
Rodney's 27 saves are the second most for any Mariners closer prior to the All-Star break, with Kazahiro Sasaki having 29 in 2001 on the way to his franchise-record 45 in that 116-win season.
The final phase of All-Star Game voting will again allow fans to help choose the Ted Williams All-Star Game Most Valuable Player Award presented by Chevrolet. During the Midsummer Classic, fans will vote exclusively online at MLB.com and via Twitter in the 2014 All-Star Game MLB.com MVP Vote Sponsored by Pepsi, and their collective voice will represent 20 percent of the overall vote that determines the recipient of the Arch Ward Trophy.
MLB.TV Premium subscribers, for the first time, will be able to live stream the All-Star Game via MLB.TV through FOX's participating video providers. Access will be available across more than 400 platforms that support MLB.TV, including the award-winning MLB.com At Bat app. MLB.com will provide extensive online coverage of the All-Star Week festivities.
The 85th All-Star Game will be televised nationally by FOX, in Canada by Rogers Sportsnet and RDS, and worldwide by partners in more than 200 countries via MLB International's independent feed. ESPN Radio and ESPN Radio Deportes will provide national radio coverage of the All-Star Game. MLB Network and SiriusXM will also provide comprehensive All-Star Week coverage. For more information, please visit allstargame.com.