That reflects a significant decline by the former House speaker since early December, when he led Obama by three points.
The poll of the dozen states likely to determine the outcome of November's election addresses the electability argument that has driven many Republicans: Which GOP contender has the best chance of denying Obama a second term?
In a head-to-head race, Romney leads Obama by a statistically insignificant percentage point, 48%-47%, the survey finds.
But Obama leads Gingrich, 54%-40%. The president's standing against him has risen nine points since early December; Gingrich has fallen by eight.
Gingrich fares less well than Texas Rep. Ron Paul, who trails Obama by seven points, 50%-43%, and former Pennsylvania senator Rick Santorum, who also trails by seven points, 51%-44%.
The Swing States survey focuses on the nation's most competitive battlegrounds: Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin.
The findings presumably reflect the barrage of attacks on Gingrich's temperament and record by Romney and other prominent Republicans, from Arizona Sen. John McCain to former Senate majority leader Bob Dole. The former House speaker has drawn fierce fire since winning the South Carolina primary on Jan. 21 and surging to the top of national polls.
In Florida, which holds its primary Tuesday, Romney led Gingrich in a Marist Poll released Sunday by 15 points, 42%-27%.
Gingrich blamed his fall on negative TV ads aired by Romney and his allies. "He has a basic policy of carpet bombing his opponent," Gingrich said on Fox NewsSunday. "It has an effect."
Romney, campaigning in Naples, Fla., said Gingrich should "look in the mirror" to see why his support has dropped.
Voters in both parties rate Romney higher than Gingrich on a series of positive characteristics. Nearly six in 10 say Romney has the personality and leadership qualities a president should have; 42% say Gingrich has those qualities. Fifty percent call Romney sincere and authentic; 38% say that of Gingrich.
Neither does particularly well when asked whether they understand the problems Americans face in their daily lives: 44% of those surveyed say that applies to each.
The survey of 737 registered voters, taken Tuesday through Saturday, has a margin of error of +/- 5 percentage points.