Firefighters and soldiers scrambled with ladders, cranes and other equipment to the two towers that folded like an accordion in a pile of rubble and twisted metal and extracted dazed survivors.
The emergency response center said that three people were killed, including a 10-day-old infant, a 55-year-old woman and a 50-year-old man.
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A second 16-story high-rise also collapsed in the same way and fell on its side, and more than 30 survivors have been pulled out from there.
Dozens more people have been rescued or safely evacuated from a market and a seven-floor building that was badly damaged, the Central News Agency reported.
A bank building also careened, but no injuries were reported, it said.
Most people were caught asleep when the earthquake struck at about 4 a.m local time (2000 GMT Friday). It was located some 22 miles (36 kilometers) southeast of Yujing, and struck about 6 miles (10 kilometers) underground, according to the US Geological Survey.
As dawn broke, live Taiwanese TV showed survivors being brought gingerly from the high-rise, including an elderly woman in a neck brace and others wrapped in blankets.
The trappings of daily life a partially crushed air conditioner, pieces of a metal balcony, windows lay twisted in rubble.
People with their arms around firefighters were being helped from the building, and cranes were being used to search darkened parts of the structure for survivors. Newscasters said other areas of the city were still being canvassed for possible damage.
Men in camouflage, apparently military personnel, marched into one area of collapse carrying large shovels.
The Taiwanese news website ET Today reported that a mother and a daughter were among the survivors pulled from the Wei Guan building and that the girl drank her urine while waiting for rescue, which came sooner than expected.
The quake was felt as a lengthy, rolling shake in the capital, Taipei, on the other side of the island. But Taipei was quiet, with no sense of emergency or obvious damage just before dawn.
Residents in mainland China also reported that the tremor was felt there. Earthquakes frequently rattle Taiwan, but most are minor and cause little or no damage.
However, a magnitude-7.6 earthquake in central Taiwan in 1999 killed more than 2,300 people.
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