In Florida, the largest swing state with 29 electoral votes, Mr. Obama leads by Romney among likely voters by 49 percent to 44 percent.
In Virginia, with 13 electoral votes, Mr. Obama leads by the same 49 percent to 44 percent margin.
And in Ohio, with 18 electoral votes, the Democratic incumbent leads his Republican challenger by 50 percent to 43 percent.
In all cases, Mr. Obama's edge was outside the polls' 3.1 percentage point margin of error.
The president's lead was build on strong support from women voters. His margin among women was 12 percentage points in Florida, 16 percentage points in Ohio, and 14 percentage point in Virginia.
Mr. Romney lead in all three states among men - but by much smaller margins. The former Massachusetts governor's edge among men was four percentage points in Florida, two percentage points in Ohio, and five percentage points in Virginia.
One key to Mr. Obama's strong showing in the NBC/WSJ/Marist polls is his competitiveness on the number one issue in Mr. Romney's campaign: the economy.
Only in Florida do likely voters say Mr. Romney would better handle the economy — by a slender 47 percent to 44 percent. In Ohio and Virginia, likely voters give Mr. Obama a narrow edge on the issue.
Meanwhile, Mr. Obama enjoys double-digit advantages in all three states on handling foreign policy — a topic of rising interest in the campaign amid attacks on US diplomats in Libya and Egypt.
Lee Miringoff of Marist noted that the intensity of voter preferences and the small number of undecided make this contest in mid-September feel like previous campaigns felt in mid-October.
"It's a campaign of mobilization, not a campaign of persuasion, Mr. Miringoff said. He added: "You'd much rather be in Obama's shoes than Romney's in these critical states."
Mr. Obama carried all three battlegrounds over Republican John McCain in winning the presidency four years ago. Republican strategists consider all three important bellwethers of Mr. Romney ability to amass the 270 electoral votes needed to win.
- By CNBC's John Harwood