The poll comes less than three weeks after a Boston Herald/Franklin Pierce poll in New Hampshire on August 11 showed Sanders leading Clinton, 44-37, in that state.
Still, Clinton maintains a broad national lead. She led Sanders by 23 points in a Quinnipiac poll early this week.
The seven-point margin is Clinton's smallest lead in Iowa this election cycle, and her 37 percent support is her lowest showing in the state since the campaign began.
"What this new poll shows is that the more Iowans get to know Bernie the better they like him and what he stands for," Sanders spokesman Michael Briggs said. "We’ve seen the same thing in New Hampshire and across the country."
The numbers show more of a decline in support for Clinton than an increase in support for Sanders. Other polls this summer have shown Sanders hovering around 30 percent in Iowa. But in the past, Clinton has garnered support from roughly half of Iowans.
That leaves a rather high 14 percent of likely Democratic caucus-goers in Iowa unready to choose a candidate at this point.
The poll also finds that among voters under 45 years old, Clinton is losing to Sanders by a broad 23 points.
Meanwhile, on the Republican side, Donald Trump maintains his lead in Iowa with 23 percent, although neurosurgeon Ben Carson is closing the gap, up from 10 percent in a May Bloomberg/DMR poll to 18 percent now.
Wisconsin Gov. Scott Walker, who had been leading in Iowa earlier this summer, seems to be fading back into the pack, tying with Texas Sen. Ted Cruz for third with only 8 percent support. Former Florida Gov. Jeb Bush and Florida Sen. Marco Rubio were tied with 6 percent support, while former HP CEO Carly Fiorina clocked in with 5 percent.
A broad six in 10 likely Iowa caucus-goers said they see Trump favorably, compared to only 45 percent for Jeb Bush. Meanwhile, four in 10 likely Iowa Republican caucus-goers say they would never vote for Bush, while only three in 10 say the same of Trump.
The poll also shows a strong anti-establishment bent: Trump, Carson, Cruz and Fiorina combine for a whopping 54 percent of the GOP vote, while establishment candidates like Bush, Walker, Rubio and Ohio Gov. John Kasich combine for only 22 percent.