"It's stuff you dream about," said Giambi, still out of breath after the mob scene in Cleveland.
The Indians have larger dreams in mind, and that is why this improbable win within an even more impossible season was so critical.
Cleveland has overcome so much this season to soar up the standings this September into the American League's second Wild Card seed, which they still hold with a one-game lead over Texas.
If one game could sum up a season, this was it. It was a roller coaster that began with a strong start from Ubaldo Jimenez and nearly ended when closer Chris Perez surrendered a pair of ninth-inning home runs to push the Tribe to the brink of a demoralizing defeat.
That outcome did not fit the script of this storybook season.
"That had to have been, by far, one of the more emotional wins that we've had," Indians first baseman Nick Swisher said. "Especially considering where we are in the running. If you lose that game, man, you never know what's going to happen. We're in that position right now where we've got to win out. We've got to win.
"I almost started crying when he hit that ball."
Giambi's blast off White Sox closer Addison Reed marked the 11th walk-off win of the season for the Indians, who have rattled off 10 wins in their past 12 games. It gave the 42-year-old slugger three pinch-hit homers this season, tying a franchise record most recently achieved by Ron Kittle in 1987. Cleveland collected its 13th consecutive win over Chicago and its sixth win against the White Sox in the last at-bat.
Cleveland's magic number to clinch a Wild Card spot current sits at five.
With Chicago clinging to a 4-3 lead in the bottom of the ninth, Indians manager Terry Francona called upon Giambi with Michael Brantley standing on first base. Cleveland brought the veteran into the fold to be a leader within the clubhouse, but the Indians also had this exact situation in mind. Giambi might be long in years, but his swing is still long in power.
"He's always ready," Francona said. "And that's why he's playing this game, because he wants to win, and he's willing to do anything for anybody at anytime. Fortunately for us, sometimes it's when he steps in the batter's box."
Brantley stole second base and Giambi surveyed the shift and considered trying for a "dribbler to short," but everyone else in the stadium hoped, begged, prayed for more.
"I was on the top step with Tito," said second baseman Jason Kipnis, referring to Francona. "We were both like, 'One more time. One more time. Just lightning in a bottle. Come on. Get it one more time.'"
Giambi got a 1-1 slider that darted down toward his barrel, and he did not miss.
"Boy did he hit that ball," Francona marveled. "Wow."
"Oh my gosh," Swisher said with his eyes wide.
"He put such a great swing on that ball," Brantley said. "I was on second base, and as soon as he hit it, I knew it was a home run. I jumped up and down. I fist-pumped. The guys were making fun of me for how I reacted. I don't even remember hitting third base. I was so excited."
"Yeah, I ran into it," Giambi said with a grin. "God. There's nothing more special. That's what keeps you coming back every year."
As the baseball soared into the Cleveland night, nothing that preceded it mattered.
Jimenez gave the Indians 6 1/3 solid innings, striking out seven, allowing two runs, and now has a 1.86 ERA since the All-Star break. He was bailed out by Brantley, who launched a game-tying home run off White Sox lefty Hector Santiago in the seventh. Kipnis then gave the Tribe a short-lived 3-2 lead in the same frame with a run-scoring single off reliever Nate Jones.
Trying to nail down the win in the ninth, Perez turned and watched helplessly as Dayan Viciedo deposited one of his pitches over the wall in right field for a leadoff home run that tied the game at 3-3. Three hitters later, Alejandro De Aza belted an offering to deep right-center, giving Chicago a 4-3 advantage and causing the crowd to erupt in a chorus of boos. The closer, eyes fixed on the ground, trudged off the field.
"He was a little down and I gave him a big hug," Giambi said. "He's going to be a huge part of us all the way down the stretch. If we get an opportunity to play in the playoffs, we need him."
It will be easier for Perez to turn the page, and all of Cleveland for that matter, given the way Tuesday night ended.
Giambi tore around third base and stutter-stepped as he entered the bouncing mob that awaited him at home plate. He was doused in water and nearly lost his jersey as his teammates pulled, pushed and pummeled the latest player to step up and play hero. Kipnis jumped into Giambi's arms and, after breaking away from the pile, Giambi picked his manager up and embraced him in a bear hug.
It is moments such as these that make the Indians believe there is something special brewing.
"I've always felt that way," Francona said.
For Giambi, who has 19 seasons in the game, it was a home run he will cherish.
"It's the top of the world right now," Giambi said. "I don't even think I touched the ground."