Incumbent Republican Senate candidates hold big leads over their Democratic challengers in the crucial states of Florida, Ohio, and Pennsylvania, according to a Quinnipiac University poll released Thursday morning.

Holding the biggest lead in the poll was Sen. Marco Rubio in Florida, who is ahead of Democratic Rep. Patrick Murphy by a 13 point margin of 50 percent to 37 percent. Rubio was found to lead Democratic Rep. Alan Grayson by a slightly smaller margin of 50 percent to 38 percent.

In Pennsylvania, incumbent Republican Sen. Pat Toomey holds a 49 percent to 39 percent lead over Democratic challenger Katie McGinty. In Ohio, Sen. Rob Portman leads the state's former Democratic Gov. Ted Strickland 47 percent to 40 percent.

"The numbers seem to be breaking the Republican way in the battle for control of the U.S. Senate, at least when it comes to the critical swing states of Florida, Ohio and Pennsylvania," said Peter A. Brown, assistant director of the Quinnipiac University Poll.

Brown said the poll shows that the senators are polling ahead of presumptive Republican presidential nominee Donald Trump.

"Many talking heads have suggested that with Donald Trump at the top of the GOP ticket, Republican Senate candidates might suffer," Brown added. "But at least in these three key states, the Republican Senate candidates are running ahead of Trump and don't seem to be hurt by their shared party label."

Rubio's wide gap over Murphy is thanks to a big lead, 51 to 32 percent, among Independent voters. He is also doing far better with Republicans than Murphy is doing with Democrats.

"The breadth of Sen. Rubio's lead against Rep. Patrick Murphy, who has the backing of the Democratic leadership, is impressive," said Brown. "He has a 19-point margin among independent voters and scores 10 points better among Republicans than Murphy does among Democrats."

Portman also won the Independent vote in Ohio, 49 to 39 percent. Portman had a positive favorability margin, 40 to 32 percent, while Strickland had a slightly negative rating of 38 to 42 percent.

Pennsylvania voters indicated that they like Toomey, giving him good marks on both job approval, 47 percent to 39 percent, and favorability, 45 percent to 34 percent.

Toomey leads McGinty among both men and women. Forty-one percent of voters said they did not know enough about McGinty to have an opinion about her even though she has been running a state-wide campaign since last Summer.