Clinton also made gains on Trump in Ohio and maintained a slight lead in Pennsylvania, both also considered key states to winning the presidency.
In Ohio, Clinton tied Trump 40-40 in the June poll. This represents a boost for the Democrat, as Trump led Clinton 43-39 in Quinnipiac's May poll.
In Pennsylvania, Clinton has a 42-41 lead over Trump, almost unchanged from her 43-42 lead in the May Quinnipiac poll.
When minor party candidates are included in the questions, Clinton leads Trump in all three states.
Among Florida voters, it was Clinton 42, Trump 36, Libertarian Gary Johnson 7, and the Green Party's Jill Stein 3 percent.
In Ohio, it was Clinton 38, Trump 36, Johnson 8, and Stein 3.
In Pennsylvania, it was Clinton 39, Trump 36, Johnson 9, and Stein 4.
Quinnipiac University conducted the polls June 8-19 via phone. The university surveyed 975 Florida voters with a margin or error plus or minus 3.1 percentage points; 971 Ohio voters with a margin of error plus or minus 3.1 percentage points; and 950 Pennsylvania voters with a margin of error plus or minus 3.2 percentage points.