MINNEAPOLIS — Marco Rubio captured Minnesota on Tuesday for his first win in the march to the Republican presidential nomination, while Bernie Sanders snagged a critical victory in the state’s Democratic caucuses.

Rubio and Sanders cashed in on a late string of visits to a state that’s normally been an afterthought in the race to the nominating conventions. But both candidates still face huge climbs to snag their parties’ nod.

Hillary Clinton posted a dominant performance of southern states voting on Super Tuesday and has locked up support of hundreds of superdelegates. Rubio’s sole win came as front-runner Donald Trump padded a wide lead in the GOP field and Texas Sen. Ted Cruz won his home state and Oklahoma.

Minnesota’s proportional allocation of votes means Cruz, Clinton and others will likely add to their delegate hauls. Cruz was poised for a second place finish based on early returns.

The new interest in Minnesota’s caucuses, combined with the appeal of outsider candidates, translated into banner turnout for both parties.

Thousands of voters wound around staircases and hallways inside a Minneapolis recreation center to cast ballots for the Democratic caucus, quickly drying up the site’s supply of printed ballots and forcing officials to use scraps of notebook paper for votes. At a GOP caucus in the northwestern Minneapolis suburb of Maple Grove, caucus-goers first filled up a middle school auditorium, then packed several overflow rooms.

Several Democratic voters weighed a sense that Sanders best matched their values against a belief that Clinton might give Democrats the strongest chance to maintaining the White House. While she said the former secretary of state may be a safer bet to win in November, Amy Shaunette sided with Sanders due to his vow to tackle income inequality and his appearance on the Ellen DeGeneres show, among other factors.

“It’s all a mess,” she said. “We might as well have someone that I really believe in at the center of the mess.”

Sanders spent more time in Minnesota than any other candidate, rallying in the state’s most liberal pockets in recent days while Clinton largely relied on surrogates until last-minute trips to a Minneapolis coffee shop and marketplace.

Rubio was the lone GOP candidate to drop into Minnesota as his rivals focused elsewhere, hosting a caucus-day rally in a Minneapolis suburb after a visit last week. Steven Trobiani headed inside the Maple Grove caucus site with his mind made up for Rubio.

“Marco Rubio appears to be a candidate who has taken up the mantle of representation of the middle class, and I think we desperately need that,” the 65-year-old neurologist said.

But Trobiani noted Trump’s wide lead in the GOP race. Asked if he’d back the New York businessman as the party’s nominee, he answered: “Unfortunately, yes.”

Seventy-seven Democratic delegates were up for grabs in Minnesota on Tuesday; 38 on the Republican side. And there’s an extra 16 for Democrats in the form of so-called “superdelegates” — party bigwigs and elected officials who cast votes independent of the results. Most had already pledged their support to Clinton ahead of Tuesday’s vote.