Soriano had been tied with Roberto Hernandez, who earned 43 in 1999, when he got the final three outs to notch the record-breaker.
"I am so happy with that," Soriano said. "I didn't come here to break or tie the [saves] record. They brought me here to win. That's what I'm here for."
Soriano is now 22-for-22 in save chances at Tropicana Field this season, and he has been a huge addition to a bullpen that lacked a true closer in 2009.
"Just look at last year to know what he's meant this year. [Last year we were not] able to really close games on a consistent basis," manager Joe Maddon said. "And [it's also hard] having to parcel out your bullpen to the point where you have guys for the ninth inning. Now you just know that that's taken care of, and you try to piece things together for eight innings. That's a huge difference.
"He's just locked that thing down. ... I think that he totally changed the fabric of our bullpen."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.