Vice President Biden, who is contemplating a late entry into the race, came in third at 14 percent, while former Maryland governor Martin O'Malley was a distant fourth at 3 percent. Without Biden in the race, the poll showed Clinton leading Sanders, 43 percent to 35 percent.
In Iowa, Clinton has invested heavily in field staff, has made frequent visits and has been airing costly television advertisements. Unlike in New Hampshire, where Clinton has slipped behind Sanders in recent polls, she appeared to have been holding onto a dominant position in Iowa.
But Saturday's poll found the former secretary of state on a downward trajectory, losing a third of her supporters since May and dropping below the 50 percent mark for the first time in four Register-Bloomberg surveys this year.
J. Ann Selzer, a highly-regarded Iowa pollster who conducted the surveys, was quoted in the Register drawing a comparison to the 2008 campaign, when Clinton finished a disappointing third in the Iowa caucuses, behind Barack Obama and John Edwards.
"This feels like 2008 all over again," Selzer told the Register.
Selzer was quoted by Bloomberg as saying the Saturday poll amounted to "a wake-up call" for the Clinton campaign.
"It looks like what people call the era of inevitability is over," Selzer told Bloomberg.
The Iowa poll showed Sanders's popularity rising sharply in Iowa, where Democrats historically have had a populist streak and where his outsider message of leading "a political revolution" against "the billionaire class" appears to be catching on.
Sanders's favorability rating among likely Democratic caucus-goers jumped from 57 percent to 73 percent over the past two months, the poll found. The survey showed him attracting a coalition similar to Obama's in 2008: young people, liberals and first-time caucus-goers.