Pete Buttigieg has surged to third place in a new Iowa poll, within striking distance of Elizabeth Warren and Joe Biden, the long-term frontrunners in the race for the Democratic presidential nomination.

The poll, by Suffolk University and USA Today and released on Monday, suggested Buttigieg’s attack on Warren’s healthcare plans in last week’s debate may have paid off, at least in the short term.

Among respondents in the Iowa poll, 40% said Buttigieg’s debate performance had been stronger than they expected.

The 37-year-old mayor of South Bend, Indiana, a force in the ideological centre of the sprawling Democratic field, has also campaigned hard in Iowa, the first state to vote.

The new poll put Biden at 18%, Warren at 17% and Buttigieg, the youngest candidate in the race, at 13%.

“Iowa is unquestionably up for grabs,” David Paleologos, director of the Suffolk Political Research Center, told USA Today.

The mayor, he said, “has found a lane and is accelerating toward the front of the pack, surpassing Bernie Sanders. All of this is happening while the number of undecided voters continues to grow as Democratic caucus-goers pause to re-evaluate the changing field.”

In the poll, 29% of voters said they were still undecided.

Buttigieg appeared on the political talkshows on Sunday, commenting on the row between Hillary Clinton and campaign rival Tulsi Gabbard and, more directly, attacking Warren over her position on healthcare.

Revisiting an attack from his performance in last week’s debate in Ohio, Buttigieg told CNN’s State of the Union: “We need to see how [Medicare for All] is going to be paid for. Right now, whether you copy-paste the Bernie Sanders math or do it some other way, there is a hole amounting to trillions of dollars in how this is supposed to work.”

Warren said on Sunday she would soon release details of how she would pay for her version of Medicare for All.

Buttigieg discussed his idea, Medicare “For Those Who Want It”. On NBC’s Meet the Press, he agreed he would pay for it by “just basically roll[ing] back” Donald Trump’s “entire corporate tax cut”.

He also conceded: “Governing is easier said than done.”

On Sunday, it was reported that Facebook chief executive Mark Zuckerberg had recommended staff members to Buttigieg, a rare move in the campaign arena. On Monday, Zuckerberg said: “This shouldn’t be taken as an endorsement.”

As the field narrows – slightly – and the 3 February Iowa caucuses draw near, Buttigieg has posted strong fundraising numbers. He raised $19.1m in the third quarter of the year, down from a second quarter which brought in $24.9m but still contributing to a healthy campaign war chest.

In a Guardian analysis of donations to the Democratic candidates, released on Monday, Buttigieg came out on top among business executives, military veterans (he served in Afghanistan) and – topically – doctors.

“Pete continues to stand out as having the vision and leadership voters know we need to tackle the urgent problems facing our country,” Buttigieg’s campaign manager, Mike Schmuhl, said when the third-quarter figures were released. “It also positions us solidly as one of the top three fundraisers in this race.”

Sanders was in fourth place in the new Iowa poll, with 9%. Kamala Harris, who surged in the equivalent poll in June after a strong performance in thefirst debate of the campaign, fell to 3%. Tom Steyer, Amy Klobuchar and Gabbard were level with her.