The Washington Post/ABC poll gave him 33 per cent support among likely caucus voters in Iowa, with Romney and Texas congressman Ron Paul both on 18 per cent.
Gingrich has a similar 15-point lead in South Carolina, where Texas governor Rick Perry is third.
In Florida, where Cain was strong, Gingrich has a 25-point gap on Romney, while the latter's once-massive lead in New Hampshire has been halved to about 15 points.
Moreover, Gringrich may soon be endorsed by Cain, a friend and fellow Georgian.
The turnaround in his fortunes reflects not just activists' dissatisfaction with Romney but also a string of solid debate performances in which the veteran Washington politician has shown fluency on the issues and much less arrogance than in the past.
His priorities have changed as well. With his support now soaring, Gingrich now needs the money and organisation to match.
On Tuesday he was not in Iowa or New Hampshire but in Manhattan for fundraisers with wealthy donors, and the now obligatory call on Donald Trump - mogul, reality television host, and seeming Svengali of Republican presidential politics.
That last function appals several party strategists, who note that Trump - a leader of the "birther" campaign against Barack Obama and who has talked about his own White House bid - will return to the limelight when he hosts a candidates' debate days before Iowa votes.
Ari Fleischer, a former George W. Bush spokesman, called the debate "an invitation to a circus".
The immediate question, however, is whether Gingrich will outlast Michelle Bachmann, Perry and Cain before him, who each briefly soared to the top of the polls as the "anti-Romney" candidate before coming to grief.
Many observers predict the former Speaker will self-destruct as he has done not infrequently in his controversy-studded career.
- Independent