Southern Media & Opinion Research found Republican state Treasurer John Kennedy leading the race with 22 percent among likely voters, followed by Democratic Public Service Commissioner Foster Campbell with 16 percent.
Under Louisiana election rules, the top two vote-getters in next month's election will make it to the Dec. 10 runoff race.
Boustany is in third place at at 14 percent, followed by Democratic lawyer Caroline Fayard with 11 percent and Fleming at 9 percent.
Last month, the same poll found Boustany running a close second to Kennedy, 15 percent to 17 percent.
The latest poll surveyed 500 likely Louisiana voters by landline and cellphones from Oct. 19-21. The margin of error was 4.4 percentage points.