The survey, from Democratic firm Public Policy Polling, gives Paul 28 percent support, while Rubio takes 25 percent support. New Jersey Gov. Chris Christie has 14 percent support and Florida Gov. Jeb Bush and Rep. Paul Ryan (R-Wis.) both get 7 percent support.
Paul's support in the new poll is a steep increase from PPP's last survey of the state, in November, when he only took 4 percent support. Rubio has also seen a surge in support, up from 14 percent in November. Christie, Bush and Ryan have all seen their support decline slightly.
And while Rubio actually has a slight lead among Republicans, Paul is boosted by his appeal among independent voters, who make up a plurality of registered voters in the swing state. Paul takes 32 percent support among swing voters, while Rubio comes in third, behind Christie, with 17 percent support.
Hillary Clinton has a commanding lead for the Democratic nomination, taking 68 percent support among Democrats, to Vice President Biden's 12 percent support.
She would topple either Paul or Rubio in a matchup, by double digits, with an 11-point advantage over Paul and a 14-point advantage over Rubio.
The PPP poll was conducted among 933 New Hampshire voters from April 19-21 and has a margin of error of plus or minus 3.2 percentage points overall, 5.1 percentage points for the Democratic portion and 4.9 percentage points for the Republican portion.