An ICM Poll shows 51% for Yes with 49% for No, bucking the national trend.
The poll, which extracted 125 Glasgow residents from the overall sample of 505 people who watched the debate, also found seven out of 10 Glaswegians thought Alex Salmond was the winner in this week’s TV debate.
It found 71% of people said the First Minister was the clear winner with 29% for Alistair Darling.
IT also found 62% believed Mr Salmond to have the best arguments compared to 38% for the Better Together leader.
Humza Yousaf, Glasgow SNP MSP, said the poll findings was a breakthrough.
He said: “This is a fantastic poll which shows that people in Glasgow are completely fed up with the lack of vision from the No campaign.”