Bredesen garners 48 percent of support among likely voters, compared with 46 percent for Blackburn. Five percent of likely voters responded that they are undecided. The Democratic former Tennessee governor's edge over the GOP representative falls within the poll's margin of error.
The two candidates aim to succeed Sen. Bob Corker, a Republican and occasional critic of President Donald Trump who declined to run for a third term. The incumbent's departure and Bredesen's statewide name recognition — he served from 2003 to 2011 — gives Democrats one of their best chances to flip a Senate seat on this year's brutal Senate map.
The GOP hopes to keep or expand its 51-49 seat majority in the chamber in November. As multiple Senate Democrats face re-election this year in states Trump won overwhelmingly, Bredesen would likely need to win in red Tennessee for his party to gain the two seats needed to take a majority.
The state's leanings show why the Democrat has avoided criticizing Trump in many instances. Forty-seven percent of likely voters in Tennessee approve of the job the president is doing, compared with 43 percent who disapprove, according to the NBC/Marist survey.
Bredesen leads among independent likely voters, garnering 49 percent compared with 45 percent for Blackburn. He also does a better job than Blackburn of holding the line within his party.
The ex-governor has the support of 97 percent of Democrats, while Blackburn draws 0 percent. Meanwhile, the GOP representative has the backing of 86 percent of Republicans, compared with 9 percent of support for Bredesen among GOP likely voters.
Nine percent of likely voters answered that they might choose a different candidate on Election Day.
Blackburn has tied her political fortunes in the state to Trump's. She has run as an unabashed ally of the president, who endorsed Blackburn last month.
An ad the Blackburn campaign released last month features Trump's attacks on Bredesen made at a rally in Tennessee earlier this year.
"Phil whatever the hell his name is, this guy will 100 percent vote against us every single time," Trump says in the ad.
Likely voters in Tennessee actually hold better views of Bredesen than Blackburn, despite the state's partisan leanings, according to Thursday's survey. Sixty-one percent say they have a favorable impression of him, versus 22 percent who have an unfavorable one.
Among likely voters, 46 percent view Blackburn favorably, compared with 36 percent who view her unfavorably, according to the poll.
Bredesen, who ran a health care company before becoming governor, has touted his record expanding health-care access during his Senate bid. The outgoing senator Corker has also had kind words about Bredesen, who he worked with previously in the state.
"I'm not going to campaign against someone who I've been a friend with and worked with, you know? So that's the way it's going to be," Corker said earlier this year, noting that he gave a campaign contribution to Blackburn.
Like in other states NBC and Marist have polled in recent weeks, tariffs are unpopular in Tennessee. Trump has recently imposed the duties on leading trading partners as he seeks new trade deals.
Only 30 percent of likely voters believe the measures will shield U.S. jobs and boost the economy, while 43 percent think they will increase the cost of goods and harm the economy, according to the poll.
The NBC/Marist poll of Tennessee was conducted August 25-28 of 940 adults (which has a margin of error of plus-minus 4.0 percentage points), 730 registered voters (plus-minus 4.5 percentage points) and 538 likely voters (plus-minus 5.1 percentage points). Respondents were contacted both by landline and cell phone.