It was an easy call for Brown and there was never a doubt in the minds of anyone in the Kings' dressing room that Mitchell, 37, would be the first player other than Brown to hoist the Cup above his head and skate around the ice at Staples Center.
On Saturday, it was Mitchell's turn to return the favor to Brown and put the Kings one step closer to another trophy presentation. Midway through the second overtime, Brown redirected Mitchell's shot to give the Kings a 5-4 double-overtime win over the New York Rangers and a commanding 2-0 series lead.
As the finals head east, the win puts the Kings two wins away from winning the Stanley Cup for the second time in three years.
It's an incredible run that perhaps could have been even greater if Mitchell was with the Kings as they defended their title last season. Much was made of the Kings' keeping their entire team intact after winning the Stanley Cup. While that was contractually true, on the ice the Kings never had Mitchell, one of their defensive stalwarts and team leaders.
Mitchell was sidelined for the entire lockout-shortened season with a career-threatening knee injury that simply would not get better.
Kings general manager Dean Lombardi was even forced to make offseason plans as if Mitchell would not be back because, well, that's what you do when a 37-year-old player misses an entire season with an injury that simply won't heal.
Mitchell had two setbacks from surgery to clean up the cartilage in his knee before having an arthroscopic procedure and seeing Dr. John Mayer, who worked on Kobe Bryant's knees. Mitchell also underwent the same platelet-rich plasma therapy that Bryant popularized before he finally began to improve.
"I had a plan to get healthy and relied on one of the best guys in the business as far as rehabs on knees," Mitchell said. "I stayed down here for the summer instead of going back home and fishing like I normally do.
"When your plan works and you execute well and you comeback healthy and play a full season and you get to be a part of this, it feels darn good."
It's not the first time Mitchell thought his career might be cut short. Before he arrived in Los Angeles three years ago, concussions forced him to miss 34 games for the Vancouver Canucks. The Kings were the only team willing to commit to him for two years.
He rewarded the Kings' faith by shoring up their defense and being a role model for young defensemen like Drew Doughty and Slava Voynov. Mitchell is not as talented or as offensively gifted as Doughty or Voynov, but he gave them and the team some needed leadership.
Doughty has said on several occasions that if Mitchell had been in the 2013 playoffs, the Kings might have found a way to get past the Chicago Blackhawks and would be playing for a third straight Stanley Cup.
And even in this postseason, Mitchell had to once again come back after missing eight games with a lower body injury. He returned for the start of the Western Conference finals, where the Kings avenged last year's loss to Chicago.
As he reflected on the Kings' premature dismissal in the 2013 playoffs, Mitchell said he couldn't even watch L.A. play as it pained him too much.
"We all played hockey since we were kids and dreamed of playing in the Stanley Cup finals and winning the Stanley Cup," Mitchell said. "We have an awesome team around here. And when you're not able to do that and you want to do that and it's out of your control because health is out of your control, it's tough.
"Personally, I just disconnected from it. I didn't even watch a lot of the playoff games because it's like sticking a knife in you.
"It's nice to be back and be a part of it."
Mitchell isn't just a part of it, he's a big reason why the Kings are two games away from winning it all again. He is stabilizing presence on defense and in the dressing room and finds a way to make a difference offensive when the postseason comes around.
Mitchell's power-play goal in the second period Saturday cut the Kings' deficit to one score at 3-2 and gave him his second power-play goal in 86 career playoff games. (He has zero in 795 career regular-season contests.)
"We missed him last year, him being out," Brown said. "It changed the dynamic of the back end. Where I think he makes a very big difference, obviously, is his defensive coverage, PK. He's very hard to play against down low.
"You know, tonight, you get an added bonus with him making a difference on the offensive side of the puck, but his bread and butter is down low and PK."
When Brown tipped Mitchell's shot past Henrik Lundqvist to end the second overtime period and give the Kings yet another comeback win this postseason, L.A. players on the ice immediately gathered around Mitchell.
"He was a big part two years ago and we missed him last year," said Anze Kopitar, who was the first player to skate to Mitchell after Saturday's winning goal. "And now he's a big part again this year."