The ICM poll for Scotland on Sunday shows growth of four percentage points for Yes since last month, while No rose two points, and undecided voters fell seven points.
Of the 14% who were still officially undecided, they told the pollsters they were more likely to vote No by a ratio of 2:1.
When the undecideds were stripped out, the headline figure was Yes 45% (+2) and No 55% (+2).
ICM also asked its sample of 1,005 adults across Scotland what they thought of SNP currency policy: 52% said it was "unconvincing", 26% were convinced, and 22% were undecided.
Writing on the What Scotland Thinks website, polling expert Professor John Curtice, of Strathclyde University, said: "Today's poll puts Yes on 38%, up four points on a month ago.
"No are on 47%, also up on last month but by a more modest two points. Don't Knows (which have tended to be relatively high in ICM's polls) have fallen by no less than seven points from 21% to 14%, suggesting that undecided voters have indeed begun to make up their mind as polling day approaches.
"Once the Don't Knows are excluded the Yes tally stands at 45%, No at 55%, representing a two point swing from No to Yes since last month. A movement of that size is too small for us to be able to rule out the possibility that it has simply occurred by chance, and in any event it simply puts the Yes vote back to where it was in ICM's poll in June.
"Today's poll is thus best regarded as failing to show that No has gained any longer-term advantage from the leaders' debate than as evidence of a renewed swing to Yes."