— President Ma Ying-jeou of Taiwan won reelection Saturday, cruising to a comfortable victory that should soothe Beijing and calm worries in Washington that the island — a rambunctious democracy just over 100 miles from China — might back away from a policy of detente with its giant, authoritarian and increasingly well-armed neighbor.

“We’ve won,” Ma shouted to supporters at a rain-drenched victory rally outside the headquarters of the ruling Kuomintang, or KMT, in Taipei, the capital. Promising to continue on a path of rapprochement with Beijing begun in 2008, the Harvard-educated victor said his second term would bring “more harmonious” relations with China and reduce “the chances of conflict.”

He defeated Tsai Ing-wen of the Democratic Progressive Party, which Beijing views with deep mistrust because of its commitment, at least on paper, to eventual independence for Taiwan, which China claims as its own territory.

Tsai, a cerebral lawyer who studied at Cornell University and the London School of Economics, muted discussion of Taiwan’s status during the campaign, focusing instead on Taiwan’s widening gap between rich and poor and problems such as housing.

“Both China and the U.S. are breathing a big sigh of relief,” said Su Chi, the head of Taiwan’s National Security Council during Ma’s first term and now director of Taipei Forum, a think-tank. Taiwan, he added, “is the only place that can drag the two largest nuclear armed countries” into war, so neither Beijing nor Washington “wants to rock the boat.”

China kept mostly kept quiet during the campaign — in contrast to earlier elections when it staged missile tests, sent fighter jets into the Taiwan Strait and made verbal threats — but made clear that it preferred Ma.

The People’s Daily, the official mouthpiece of China’s ruling Communist Party, welcomed Ma’s victory in commentary posted on its Web site.

Taiwan’s orderly election process — in which a new legislature also was selected — nonetheless delivered a rebuke to the Communist Party, which has long sought to present democracy as a recipe for chaos and a Western import incompatible with Chinese values. Taiwan used to have a highly authoritarian regime but is now the Chinese-speaking world’s most vibrant democracy.

Ma, who was born in Hong Kong to parents who fled Mao Zedong’s 1949 communist revolution, has made warmer ties with Beijing a priority, reaching 16 agreements to expand economic and other links between the two former enemies.

His win, said Yen Chen-shen of the Institute of International Relations at Taiwan’s National Chengchi University, shows that “Beijing doesn’t need to use missiles but can buy Taiwan through business.”

Taiwan’s business community, which has invested billions in China, overwhelmingly supported Ma, who initiated direct flights with the mainland. More than 200,000 Taiwanese who work in China, many as factory managers and traders, flew home to vote.

Ma won 51.6 percent of the tally, less than the 58 percent he got in 2008 but still a solid win over Tsai, who received 45.6 percent. James Soong, a defector from the KMT, got 2.7 percent. The KMT also held on to the legislature, although with a reduced majority.

A victory by Tsai would have rattled Beijing at a time when Chinese leaders are especially jittery ahead of a leadership transition later this year. It could also have complicated Washington’s efforts to reassure China about its intentions after a “pivot” in American diplomacy toward Asia and the unveiling last week of a new U.S. defense strategy focused on the Asia-Pacific region. China suspects a U.S. push to “contain” its growing power.

The Obama administration didn’t openly take sides in the election, but took steps that were widely seen here as signaling a preference for Ma. These included a flurry of recent visits by senior officials and an announcement that Taiwanese citizens, who make about 400,000 visits to the United States a year, will probably be included in a visa-waiver program.

“The administration liked the fact that tensions had been reduced across the Taiwan Strait . . . and rewarded Ma,” said Douglas Paal, vice president for studies at the Carnegie Endowment for International Peace who, from 2002 to 2006, served as director of the American Institute in Taiwan, Washington’s de facto embassy in Taipei.

Ma’s win, said Paal, will be a relief to Washington as it means “there will not be a new and undetermined element” that could raise tensions and hurt chances of “Chinese cooperation on North Korea, the South China Sea and Iran.”

Paal stirred a flap on the eve of Saturday’s election when he suggested in an interview with a Taiwanese television station that Washington didn’t like Tsai’s policy toward China and wanted Ma to win. Tsai’s supporters worried that this would be taken as an American government endorsement for the incumbent. The leader of a group of foreign election observers, former Alaska senator Frank Murkowski, denounced Paal’s comments.

Paal, who is visiting Taiwan, said he was speaking only for himself. The incident nonetheless caused discomfort at the American Institute in Taiwan, whose current director abruptly canceled a meeting with Paal scheduled for election day.