The results show the challenge facing Trump, who must compete in all three states to claim the 270 electoral votes he needs to defeat Clinton.
According to the polls, in Florida Clinton is at 46% to Trump's 45%. She leads 49% to 45% in Ohio and 52% to 42% in Pennsylvania.
It's the first time the polling outfit has surveyed likely voters -- rather than registered voters or all Americans -- in the 2016 election cycle, so the results can't be compared to previous Quinnipiac surveys.
With Libertarian Party nominee Gary Johnson and Green Party nominee Jill Stein added to the race, the equation doesn't change much.
Florida is tied, with Clinton and Trump each at 43%, Johnson receiving 7% support and Stein at 3%. In Ohio, Clinton leads 44% to Trump's 42%, with Johnson at 8% and Stein at 3%. And in Pennsylvania, Clinton tops Trump 48% to 39%, with 7% going to Johnson and 3% to Stein.
The pollsters said both Clinton and Trump supporters are motivated by their negative feelings for the opposing party's candidates.
"It is not that her voters are in love with Secretary Clinton -- they just dislike her less than they disdain Trump. In fact, among Clinton voters in all three states more than 4-in-10 say their opposition to Trump, rather than their liking of her, is the main reason for their vote," said Peter A. Brown, assistant director of the Quinnipiac University Poll, in a statement accompanying the results.
"Among Trump voters, dislike of Secretary Clinton is even a larger factor in their choice. Among Trump voters, well over half say they back him because they dislike her," Brown said.
The results in Pennsylvania and Ohio largely match other recent polling in the two Rust Belt states. In Pennsylvania, a recent Suffolk University poll had Clinton ahead by 9 points, and a Franklin and Marshall poll showed her leading by 11 points in the Keystone State.
But Florida diverges from other recent poling. Both Suffolk's post-convention poll and an NBC/Wall Street Journal/Marist pre-convention survey had her up by significant margins.
The polls were all conducted July 30-August 7. The Florida poll included 1,056 likely voters and has a margin of error of plus or minus 3 percentage points. The Ohio poll of 812 likely voters includes a margin of error of plus or minus 3.4 points. And the Pennsylvania survey of 815 likely voters has a margin of error of plus or minus 3.4 points.