But the numbers also show that Moore still has a lot of ground to make up.
PPP surveyed 521 likely Democratic primary voters on March 17. Perdue was the choice of 44 percent, while Moore was the favorite of 34 percent. The poll had a margin of error of plus or minus 4.3 percentage points.
Dean Debnam, president of PPP, attributed Moore's rise to a new television ad he has been airing recently.
"That's the power of television," Debnam said.
The poll found that almost half of those surveyed remembered seeing ads for Perdue and Moore in the last week. But 14 percent said they only remembered seeing ads for Perdue, while 8 percent said they only favored seeing ads for Moore.
The poll found that Dennis Nielsen was the choice of 3 percent of those surveyed, while 19 percent were undecided.