The awards were attended by Hilton just hours before she was jailed for violating probation on an alcohol-related drink-driving conviction.
"I said some very hardcore jokes about her.... Paris, I am really sorry," Silverman said.
Hilton responded by saying she was "shocked... and pleasantly surprised".
She added: "[Silverman] was so genuine and so sweet and it really moved me. I felt emotional hearing it and I could tell she really did mean what she said when she was apologising.
"Thank you, I really, really appreciate you doing that."
Much of Silverman's 2007 monologue is too explicit to repeat, but when she said "Paris Hilton is going to jail", the audience whooped and cheered. The footage then cut to Hilton looking extremely uncomfortable.
Silverman shared her lengthy (and expletive-laden) apology on Instagram after Hilton said in her podcast earlier this week that the "cruel" jokes had left her fighting back tears, adding "this would never happen today".
Hilton recalled being" seated ringside at my own surprise public humiliation".
She said: "I was obviously very nervous... I knew I was about to check myself in to jail in a couple of hours... just getting all dressed up, going there, trying to be brave. And then to sit in the audience with her publicly humiliating me, being so mean, so cruel.
"I was sitting there wanting to die... I was trying to hold back my tears so hard. I had tears welling in my eyes, I wanted to run out of the entire room, but I just was trying to be strong and sit there, and the whole audience is laughing and she would not stop. It was so painful."
Hilton went on to serve three days of her sentence but was released early due to a confidential medical problem. She was then kept under house arrest for 20 days and had to wear an electronic tag for 40 days. Her arrest was for driving under the influence, for which she was given probation. She had violated several times by driving with a suspended licence.
The socialite was jailed at the Century Regional Detention Centre in Lynwood, California, where her lawyer said she spent 23 hours a day in a solitary cell.