The poll of 601 likely voters, surveyed between Aug. 31 and Wednesday, Sept. 7, shows Rubio holding a 50 percent to 43 percent advantage.
Rubio and Murphy, a congressman from Jupiter, both easily won their party primaries Aug. 30. A poll released Aug. 11 by the Connecticut-based Quinnipiac showed Rubio leading Murphy by a margin of 48 percent to 45 percent in a head-to-head matchup.
After failing to win the Republican presidential nomination this year, Rubio decided in June to seek a second term in the Senate.
"Democrats hoped they could use Sen. Marco Rubio's change of heart on running for re-election against him, but so far the former presidential candidate has been able to keep a narrow lead," Peter A. Brown, assistant director of the Quinnipiac Poll, said in a prepared statement Friday. "Without Rubio's double-digit lead among independent voters, he would be in much more trouble."
While both candidates have largely locked down voters in their own parties, Rubio is up 53-37 percent among independents.
In the August poll, Rubio held a 10-percentage point advantage among likely voters without party affiliation.
The latest poll also shows that racial and gender gaps apparent in this year's presidential race also are taking hold in the Senate contest.
Rubio holds a 55-35 percent advantage among men and a 56-37 percent lead with white voters. Murphy is up 51-45 percent among women and 56-38 percent among non-white voters.
The poll, which has an overall margin of error of 4 percentage points, came as Murphy and Rubio exchange barbs over the inability of Congress – back in Washington this week after a summer recess – to agree on funding to fight the mosquito-borne Zika virus.
Murphy contends Rubio hasn't worked hard enough to sway his party leaders to approve a bill that is strictly focused on President Barack Obama's request for $1.9 billion in funding. Rubio has pointed to Murphy's opposition to a House measure that included $1.1 billion for the Zika fight. The House effort also included provisions dealing with contraception, pesticides and the Confederate flag.
In ads this week, Murphy has tried to showcase a more moderate tone while reviving questions about Rubio's attendance record in the Senate. The Rubio campaign has hit back by revisiting stories that raised doubts on Murphy's professional résumé while contending Murphy would be a "rubber stamp" for Democratic presidential candidate Hillary Clinton.
Quinnipiac, which frequently surveys voters in swing states, also released poll numbers Friday for Senate contests in Ohio, Pennsylvania and North Carolina. In each state, the GOP candidates held an edge.
"The U.S. Senate races in Florida, North Carolina, Ohio and perhaps Pennsylvania show Democrats face an uphill climb," Brown said. "All four GOP candidates are running ahead of Republican presidential nominee Donald Trump, some by just a bit, but some substantially."
Backed by growing support from independent voters, Republican U.S. Sen. Marco Rubio has opened a seven-point lead over Democratic challenger Patrick Murphy, according to a poll released Friday by Quinnipiac University.