BERLIN — Chancellor Angela Merkel of Germany received a significant lift to her re-election bid on Sunday when her party finished a clear first in a state election that was widely watched as a test of her strength.

Results from Sunday’s vote in tiny Saarland, which borders France and is home to around one million people, showed that Ms. Merkel’s center-right Christian Democrats had won 40.7 percent of the vote.

The popular Christian Democrat governor of Saarland, Annegret Kramp-Karrenbauer, who secured the win, is such a close ally of the chancellor that she is often called “the mini-Merkel.” So Sunday’s election also seemed a victory for Germany’s leader.

Ms. Merkel is seeking a fourth term in national elections on Sept. 24, a race that has grown more challenging in recent weeks after her center-left rivals, the Social Democrats, unanimously selected a new candidate, Martin Schulz, to lead them into the fight.