Sosa then turned his focus to the task at hand, which is keeping the Baltimore Orioles in first place.
Sosa hit his 583rd home run to pull even with McGwire for sixth place on the career list, part of a six-run fourth inning that carried the Orioles past the Colorado Rockies 7-2 on Saturday night.
Sosa's homer off Byung-Hyun Kim was an opposite-field shot that cleared the 25-foot scoreboard in right field. It was the ninth home run of the year for the former Chicago Cubs slugger, who waged an unforgettable race against McGwire to be the first to break Roger Maris' single-season record of 61.
"In 1998, the year Mark and I went head to head, that was a privilege for me to be there with him," Sosa said. "And now he's retired, he's sitting home relaxing. To have a chance to tie him today, it's very nice."
McGwire finished with 70 homers that year; Sosa had 66. The record was broken in 2001 by Barry Bonds, who hit 73.
Sosa's mission this season is to guide the Orioles into the playoffs for the first time since 1997, so he didn't dwell on his place in baseball history.
"Right now there's no time to celebrate thinking about it, because we're on a mission, you know," he said. "Nobody expected us to be in first place, and we're still here. We're just going to continue fighting, fighting every day.
"I'm still playing. My career is not going to stop here," he said.
Sosa now needs 17 home runs to become the fifth player in major-league history to hit 600. After striking out three times Friday, he went 2-for-4 with a double and scored two runs.
"To have a chance to tie Mr. McGwire today is incredible," Sosa said. "I know I can go more, I know I can do more."
Baltimore's Rafael Palmeiro singled twice to move within 21 hits of joining Hank Aaron, Willie Mays and Eddie Murray as the only players in major-league history to have 3,000 hits and 500 homers.
But this night was about Sosa, who played with Palmeiro on the Texas Rangers in 1989.
"He's moving up the charts quickly. He'll get to 600 before you know it," Palmeiro said. "When he gets on a roll, we're going to have some fun watching him."
Sidney Ponson (7-4) gave up two runs and nine hits in seven innings for the Orioles, who have won four of five. He struck out six and walked none.
"We were a little overmatched tonight, and not too many of our guys are hot. When that happens, it usually goes the pitcher's way," Colorado manager Clint Hurdle said.
Miguel Tejada led off the fourth with his 19th home run to put Baltimore up 1-0. Three pitches later, Sosa performed his trademark hop at the plate an instant after sending the ball toward the flag court beyond the wall in right.
Palmeiro followed with a single and went to third on a double by Jay Gibbons before B.J. Surhoff and Sal Fasano hit RBI singles. After Larry Bigbie drew a walk, Brian Roberts chased Kim with a two-run single.
Kim (1-6) gave up six runs and nine hits in his third start since joining Colorado's rotation. He allowed a total of four runs over 12 innings in his other two.
"He didn't have a slider, he had nothing much but a fastball, and he was up way more than down. That's a tough combination," Hurdle said. "He couldn't change speed or direction, and he didn't locate the ball that well."
Baltimore made it 7-0 in the fifth when Sosa hit a one-out double and scored on a single by Palmeiro.
Garabito, a former Orioles minor-leaguer, hit a two-run shot in the seventh.
The Orioles have hit back-to-back homers eight times this season. ... Colorado is 1-16 on the road when scoring fewer than three runs. ... Every Baltimore starter had at least one hit by the
fourth inning. ... The Orioles have averaged 7.6 runs in Ponson's 14 starts. ... Baltimore activated outfielder Luis Matos from the disabled list after the game and optioned outfielder David Newhan to Triple-A Ottawa.