Elon Musk was shown on a large screen as Alice Weidel, co-leader of the Alternative for Germany party, spoke last month at a lectern, far right, in Halle, Germany.Credit…Sergey Ponomarev for The New York TimesThe hard-right Alternative for Germany, or AfD, doubled its vote share from four years ago, largely by appealing to voters upset by immigration. In the former East Germany, it finished first, ahead of Mr. Merz’s party.

The AfD’s vote share appeared to fall short of its high-water mark of support in polls from a year ago, however. Many analysts had been expecting a stronger showing, after a sequence of events that elevated the party and its signature issue.

The AfD received public support from Mr. Vance and an endorsement by the billionaire Trump adviser Elon Musk. It sought to make political gains out of a series of deadly attacks by migrants in recent months, including in the final days of the campaign.

But that boon never materialized.

The surprise of the night

Reaction to the recent attacks and the support from Trump officials may have even mobilized a late burst of support to Die Linke, the party of Germany’s far left, which campaigned on a pro-immigration platform, some voters suggested in interviews on Sunday.

Two months ago Die Linke was dying. Sahra Wagenknecht, its most popular member, started a new party last year that was more friendly to Russia and tougher on migration. Many followed her, thinking that she was the future. Die Linke languished at 3 percent.

But Die Linke managed to turn things around in just months, thanks to a new pair of charismatic and social-media savvy leaders and the alienation that many young voters feel with mainstream parties. It surged to what appeared to be nearly 9 percent of the vote and more than 60 seats in Parliament.

Its campaign events started attracting so many young people that they became must-see affairs, as much dance party as political rally.

The party leaders became social media stars. Heidi Reichinnek, who is credited for much of the turnaround, told a crowd on Sunday night that they owed their success to the many volunteers who went from door to door talking to people about pocketbook issues. Ms. Reichinnek told supporters they “did everything right.”

Scholz is out, but his party marches on.

Despite polling predicting his third-place finish, Chancellor Olaf Scholz had insisted until the very end that he would somehow retain his job. He was wrong. His Social Democratic Party won a record-low 16 percent, coming in third place. Though Mr. Scholz will continue as a caretaker chancellor until Mr. Merz is sworn in, he is widely expected to step down from active politics. …