Mr. Warner leads Mr. Gillespie, a former chairman of the Republican National Committee, 44 percent to 38 percent, according to the automated poll from the Republican firm Harper Polling conducted for the conservative-leaning American Action Network.
Mr. Warner, first elected to the Senate in 2008, has held double-digit leads in other public polling on the race, but Mr. Gillespie and Republicans have been counting on public dissatisfaction with President Obama’s health care law to put the seat in play.
Fifty-two percent of likely voters in the poll have an unfavorable view of Obamacare and 37 percent have a favorable view.
News of the poll was first reported by Politico.
Three other Republican candidates have filed to vie for the GOP nomination at a convention in Roanoke in June: Capitol Hill policy adviser Tony DeTora, retired Air Force pilot Shak Hill, and businessman Chuck Moss.
The automated telephone survey of 936 likely 2014 voters was conducted from Feb. 4-5 and has a margin of error of 3.6 percentage points.