Khalid Alahmadi, 23, took advantage of the 19-year-old's "vulnerability and intoxication" on 24 September 2015, a jury heard.
She said she recalled becoming conscious while slumped against a tree as Mr Alahmadi was pressed against her.
He denies sexual assault and the trial at Newport Crown Court continues.
On Tuesday, the jury was told the alleged attack took place in Gorsedd Gardens in front of the national museum in Cardiff.
The student told the court she spent the night with friends at the Tiger Tiger nightclub.
She said she recalled meeting people and dancing, but because of the amount she had drunk, she had a limited recollection of what happened at the end of the night.
Prosecution barrister Matthew Cobbe told the jury Mr Alahmadi became aware of the woman's "vulnerability and intoxication and took advantage of that".
He said Mr Alahmadi intentionally touched the woman in a sexual way without consent and without believing she consented.
When interviewed by police, the woman said she had been "very drunk"  and "unable to hold myself up".
She said when she came to, she ran away and the man made no attempt to follow her.
When she arrived at a friend's house, she said what had happened and her friend contacted the police.

The incident happened at Llanymynech near the Cross Keys hotel on Saturday, affecting the A483 until it reopened at about 15:00 BST.
Dyfed-Powys Police said highways officials had put a diversion in place after the collision on the adjacent B4398 road.

Launching on 10 November, it'll show a range of on-demand programmes including interviews, Live Lounge performances and documentaries.
There will also be a 15-minute weekly wrap up show hosted by Chris Stark called ICYMI (In Case You Missed It).
The Official Chart Bite will be another weekly show presented by YouTube stars Jack and Dean.
The station says the move will make the network's distinctive content available to even bigger audiences of young people.
Radio 1 and 1Xtra's controller Ben Cooper said: "If you love music, if you love star studded interviews, then you will love Radio 1's new programmes.
"I can't wait for us to represent visually the energy and diversity of young people's culture in UK society."
Each week, a Radio 1 DJ will also put together their top five things to watch on BBC iPlayer.
Other content available for the launch of Radio 1 on BBC iPlayer includes three track Live Lounge sessions and exclusive interviews from Royal Blood and Taylor Swift.
There will also be a 2011 Live Lounge special from Adele featuring six tracks from the archive as well as a 20-minute programme featuring highlights and never before seen footage of Zoella and ThatcherJoe during their recent Internet Takeover.
A collection of three programmes from Radio 1's Teen Awards, including Dan and Phil's round-up of the event, will also appear on the station's section of the catch-up service.
Performances from Radio 1Xtra Live in Birmingham and two special interviews, 1Xtra's Semtex meets Rick Ross and Trevor Nelson meets Mary J Blige, will also be made available after the launch.
Follow @BBCNewsbeat on Twitter and Radio1Newsbeat on YouTube

The rider, who is believed to be a 47-year-old man from the Askam area, was riding a Triumph motorbike when he collided with a Scania HGV shortly before noon on the A595 near the Askam brickworks.
Cumbria Police said the biker died at the scene. The 52-year-old man driving the HGV was uninjured.
The road was closed for several hours and police are appealing for witnesses.
A student has described coming to as a man was attacking her in a Cardiff park after a night out during freshers' week.
[NEXT_CONCEPT]
A two-vehicle collision closed a main road leading to hold-ups in Powys.
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Radio 1 has announced some of the content which will appear on the station's section of BBC iPlayer.
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A biker has died after a collision with a lorry in Askam-in-Furness.