By Fabian Cambero

SANTIAGO, Nov 22 (Reuters) - Former student protest leader and leftist lawmaker Gabriel Boric faces an uphill battle persuading voters from the vanquished centrist parties to back him rather than his hard right rival when Chile holds a presidential run-off election next month.

The 35-year-old former law student, leading a leftist coalition of the broad Frente Amplio and the Communist Party, was runner-up in a first-round vote on Sunday night, behind ultra-right rival Jose Antonio Kast.

The two will compete head-to-head in a Dec. 19 ballot, where winning over centrist voters will be key.

"In order to win the second round we must be humble and receptive," Boric said to supporters after the results came in on Sunday night, adding that held out belief that "hope wins over fear". He acknowledged he needed to broaden his support.

"We have to expand it and go out to bring people in from far beyond our boundaries."

Boric, who rose to prominence leading student protests in 2011 demanding better and cheaper education, has tapped into public anger at Chile's "neoliberal" market-oriented policies, widely considered to have helped drive decades of rapid economic growth but also stoked inequality.

That imbalance sparked off widespread angry social uprisings in 2019, which in-turn lit the fuse for the political rise of the progressive left and the redrafting of the country's Augusto Pinochet-era constitution.

"If Chile was the cradle of neoliberalism, it will also be its grave," Boric said when he won the candidacy for his leftist bloc. "Do not be afraid of the youth changing this country."

A native of Punta Arenas, in Chile's far south, he had led the Federation of Students at the University of Chile in Santiago.

By 2014 Boric, still in his twenties, had joined the national Congress as a lower house lawmaker representing Chile's vast and sparsely populated southernmost region of Magallanes.

With thick black hair and a trimmed beard, he is more groomed now than in his disheveled student leader days. Although a known face of the left in Chile, Boric was initially a dark horse candidate for the presidency.

He just reached the threshold of 35,000 signatures needed to be a candidate. But then he beat out the popular capital mayor Daniel Jadue - of the Communist Party - to lead the leftist alliance.

Boric tempered his tone as the first round of the presidential election neared, as did Kast.

He has also looked to distance himself from some more extreme views from far-left groups in his alliance, including support from the Communist Party for the Venezuelan government of President Nicolas Maduro.