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Damon Thompson was booked for attempted murder and is being held on $1 million bail. The 20-year-old student is believed to have been the victim's laboratory partner.
No details have been released about a possible motive in the attack.
UCLA police responded to a call of a stabbing in an organic chemistry lab on the 6th floor of William G. Young Hall at about 12:20 p.m. Thursday.
Police say the two had been working on an experiment when Thompson pulled out a knife and attacked his classmate.
"I heard somebody screaming, called 911," said teaching assistant Cyril Baida.
Staff members and students abandoned their experiments to scurry for gauze and get help. As Baida called 911, another teaching assistant applied pressure on the victim's neck to stop the heavy bleeding. Minutes later, paramedics were on the scene.
"I figured they are from organic so I thought, you know, an experiment went wrong, you know, the flask blew up or something like that. And so I figured shards might have hit her," said Baida. "Not in my wildest dreams I would have thought somebody stabbed somebody."
Baida says the victim was barely conscious. There was so much blood, even those trying to help her were feeling faint.
"I was trying to talk to him (the TA), you know, telling him, you know, he's doing well just because I didn't want him to faint. But, you know, I almost fainted before he did, he was fine," said Baida.
In the aftermath, Baida praises the TA who provided first aid.
"To see him, you know, never let go and really, just with the amount of blood, I mean, it got me dizzy and nauseous and I don't know how he held on. I mean, he really probably saved her life," he said.
An administrator told Eyewitness News that Thompson walked to the information desk on the third floor and told the clerk that he had stabbed someone and to call the police.
Baida says an argument may have sparked the attack.
The investigation is ongoing as police continue to interview witnesses.
Thompson lives with his cousins in Fontana, according to the Los Angeles Times. They told the newspaper that Thompson is not a violent person. They said he's very mellow, but he can get touchy about his belongings.
Thompson may appear in court on Monday for arraignment.
The victim's family released the following statement:
"Her parents wish to express their thanks to everyone for their concern, and also wish to extend their gratitude to the police and emergency responders and appreciation to the UCLA medical team."