In the survey released Monday by the Quinnipiac Polling Institute, 42 percent of likely Democratic primary voters said they would go for Rep. Joe Sestak and 41 percent said they preferred Specter. The poll's margin of error is 3.5 percent.
Another 16 percent said they were undecided and 25 percent of those backing a candidate said they might change their minds, with Specter's supporters more open to switching than Sestak's.
Specter, 80, who became a Democrat in 2009, is seeking a sixth term in the Senate. Sestak, 58, is a relative political newcomer who ran for Congress in the Philadelphia suburbs in 2006 after retiring from the Navy as a rear admiral.
Sestak commercials focused on Specter's late-life change of parties after polls suggested Specter would lose the Republican primary. Specter has attacked Sestak as a no-show congressman and suggested his naval record is flawed.
On the Republican side, former Rep. Pat Toomey, who almost beat Specter in 2004, is expected to be an easy winner over anti-abortion activist Peg Luksik.
Quinnipiac surveyed 951 likely Democratic primary voters between May 12 and May 16.