"I didn't want the same thing that happened when I got my 2,000th [hit], when it took a couple of games," Soriano said. "As soon as I got the first one, I just put in my mind, 'Let me swing if I see something close to home plate, try to hit another one and get it out of the way.' Thank God it happened."
Soriano became the seventh player to hit his 400th homer as a Yankee, joining a select group comprised of Babe Ruth, Lou Gehrig, Mickey Mantle, Reggie Jackson, Gary Sheffield and Alex Rodriguez.
The homers -- a three-run shot in the first inning and a solo blast in the third -- were Soriano's 10th and 11th since he joined the Yankees from the Cubs in a July 26 trade.
It marked Soriano's sixth multihomer game of the season and the 36th of his Major League career, giving him 28 homers overall this season.
"I just think about making a good swing," Soriano said. "I never try to think about hitting homers, because that never happens. I just try to make a good swing, see the ball good and try to hit it hard."
Soriano also became the sixth player in Major League history to reach 400 homers, 2,000 hits and 250 stolen bases, joining Willie Mays, Andre Dawson, Barry Bonds, Sheffield and A-Rod.
Yankees manager Joe Girardi said that Soriano has seemed to be rejuvenated by his return to pinstripes, in which he started his Major League career in 1999.
"What he's done here in the month of August, I'm sure people are talking about it," Girardi said. "There's baseball left in this guy, and he can have a really good year."
Yankees left-hander Andy Pettitte, Tuesday's winning pitcher, said that the 36-year-old Soriano has been an "energizing" force for the club.
"He looks like a young man out there," Pettitte said. "I know he's not. Hopefully, we can keep it going. He's doing a great job for us, that's for sure."
Soriano started his big league career with the Yankees in 1999 and hit 98 homers for New York before being traded to the Rangers in the February 2004 deal that brought Rodriguez to the Bronx.
Soriano hit 64 home runs in his two seasons with Texas, then enjoyed a 46-homer campaign with the Nationals in 2006 before signing as a free agent with the Cubs, with whom he slugged 181 of his career home runs.
"When I retire, I can think about what I did in the game," Soriano said. "I'm very proud. The talent that I've got, God gave it to me. I never think I'm going to hit 400 homers in the big leagues with my size, but I think I work hard and try to get better every day. That's what I've got."