Police said the 33-year-old victim was playing on a fruit machine in the Rosevale Tavern in Partick at about 18:00 on Saturday when a stranger assaulted him.
The attacker fled via a side entrance and CCTV showed him heading down Dumbarton Road towards the city centre.
The victim was taken to the Queen Elizabeth University Hospital for treatment to a serious facial injury.
Det Con Jen Adams, of Police Scotland, said: "This was a completely unprovoked attack which will leave the victim scarred for life.
"Officers have been conducting extensive enquiries including examining CCTV and speaking to people who were within the pub at the time of the incident."
The attacker is described as being aged in his mid 20s with brown hair which was longer at the top and shaved at the bottom.
He was wearing a black quilted waist-length jacket, dark blue jeans and dark trainers.

Mr Weah got 78% of the vote for the Montserrado county seat, which includes the capital Monrovia.
He beat Robert Sirleaf, the son of President Ellen Johnson Sirleaf, who took nearly 11%.
Low turnout in the poll, which was first planned for October, was blamed on concerns about Ebola.
Strict health controls were in place to try to prevent the spread of the disease.
Those who came to polling stations had their temperature taken, were told to stand a metre (3ft) apart and wash their hands before and after voting.
Liberia has been one of the countries worst affected by Ebola, with almost 3,400 deaths, the UN says.
Other winners in the senate elections include Jewel Howard-Taylor, the ex-wife of the jailed former president Charles Taylor, and the former rebel leader Prince Johnson. Both retained their seats.
The National Elections Commission chairman, Jerome Korkoya, called the conclusion of the vote "the end of a crucial journey".
Mr Weah won the first round of the 2005 presidential election, losing the runoff to Ms Johnson-Sirleaf.
He is the only African to be named Fifa's world player of the year, winning in 1995.

The Shrimps lost their opening game of the season at newly-promoted Grimsby but then knocked Championship side Rotherham out of the EFL Cup 5-4 and have won three straight league games.
"It's nice but it is early days," 40-year-old Bentley told BBC Radio Lancashire.
"You're never too high and never too low and I keep saying that."
He added: "It's important everyone keeps their feet on the ground - likewise when you have a sticky spell that everyone keeps check and sticks together."
Kevin Ellison, 37, got the only goal of the game as Morecambe's 1-0 win at Yeovil on Saturday moved them to the top of the league.
"People say about his age and this and that but if you work with him day in, day out you see how he rubs off on other people," added Bentley on Ellison. "His desire, his attitude towards training and his own recovery and own professionalism, he's a credit to himself and his family.
"A lot of young people should look at him up and down the country because he is that good at what he does."

Residents awoke from a night of colourful fireworks to find the city covered in a thick grey blanket of smog and authorities warned that pollution levels were critically high.
A man has been left scarred for life in an unprovoked attack in a Glasgow pub.
[NEXT_CONCEPT]
The former football star George Weah has won a landslide victory in Liberia's senate elections, in polls disrupted by the Ebola outbreak.
[NEXT_CONCEPT]
Morecambe must not get carried away despite sitting top of League Two, says Shrimps boss Jim Bentley.
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Diwali celebrations in the Indian capital Delhi have seen air pollution rise to hazardous levels after many firecrackers were set off.