Although Ford appeared before senators who seemed already decided whether they would vote for or against Kavanaugh, her recounting of the attack she said happened in the summer of 1982 was challenging to hear.
Thursday's hearing comes as two other named individuals have levied allegations against Kavanaugh.
Graham, who is a member of the Senate Judiciary Committee, was discussing Ford's testimony, when a woman who later identified herself on Twitter as Robyn Swirling spoke to Graham.
Sen. Patrick Leahy, a Vermont Democrat, asked Ford what her strongest memory was of the incident - something she couldn't forget.
Republicans appointed Arizona sex crimes prosecutor Rachel Mitchell to question Ford, and she led off the questioning of Kavanaugh. These boys included Mark Judge and Brett Kavanaugh. "You can't say here at the beginning".
A GoFundMe page to support Ford and pay for her security and legal expenses quickly doubled its fundraising total after it was mentioned during the hearing.
He advised moderates waffling on their Kavanaugh vote decisions to join him in supporting the judge. If Democrats gain control of the Senate, they could deny President Trump a Supreme Court nominee for the rest of his time in office.
"We're going to look back, similar to Anita Hill, and say that there are things that we could've done right as a country that we did not do", Murray said. "They don't reach the bottom-line conclusion". Republicans have criticised the way the claims emerged shortly before his confirmation hearing, claiming they are part of a Democrat plot to derail his nomination. Each time, he declined to give a yes-or-no answer. With a narrow 51-49 majority, Republicans could afford to lose only one of their own if they could not pick up any Democrats.
"FBI finds potential eyewitnesses, tries to confirm surrounding facts", and more, he said. They later announced that they still meant to vote Friday on Kavanaugh. "A court would do so under oath".
According to Ms Ford, Mr Kavanaugh assaulted her at a party in the 1980s when she was 15 and he was 17.
She said she was terrified to come forward but did so because she felt it was her civic duty.
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The death toll rose above 100 on Friday after a ferry capsized and sank on Lake Victoria, Tanzania state radio reported. Some of the deadliest have occurred in Tanzania, where passenger boats are often said to be old and in poor condition.
"Would you believe me that no study says that this setting in five-minute increments is the way to do that?" "Why would you resist that kind of investigation?"
In an election-season battle that is being waged along a polarised nation's political and cultural fault lines, Mr Trump and most Republicans have rallied behind Mr Kavanaugh.
"The friends on the other side set it up to be just the way it is", Graham said. "This damages his credibility, perhaps irrevocably".
She has said her mind is not yet made up on Kavanaugh.
You can read his full remarks below.
"Laughter - the uproarious laughter between the two", Ford, her voice wavering, told the Senate Judiciary Committee at Thursday's extraordinary hearing.
In the opening statement, Kavanaugh denied Ford's allegations and choked up when discussing his daughter telling him that they should pray for her, among several other times.
'When you see Sotomayor and Kagan tell them that Lindsey said hi because I voted for them, ' he said referring to Supreme Court Justices Sonia Sotomayor and Elena Kagan.
Chairman Chuck Grassley, an Iowa Republican, asked if he found Ford to be credible, said the committee needed to "take her very seriously".
"There is no question that Judge Kavanaugh is qualified to serve on the Supreme Court, and in a different political environment, he would be confirmed overwhelmingly", Sen.