China views Taiwan as a renegade province and since 1979 the US has acknowledged Beijing's claim that Taiwan is part of China, with US-China relations governed by a set of protocols known as the One China Policy.
Taiwan's President Tsai Ing-wen on Friday night published a statement about the 10-minute phone call, in which the two shared views on policies.
China's state-run CCTV quickly issued a statement following the call saying the President-elect had made "an unprecedented break with the One-China Policy and accepted US-Mainland protocol."
Trump -- who has previously vowed to take a tough line towards Beijing -- stressed that Taipei had initiated the call.
"The President of Taiwan CALLED ME today to wish me congratulations on winning the Presidency. Thank you!" he tweeted.
Zhang Baohui, a political science professor at Lingnan University in Hong Kong, said the tweets made it clear that Tsai had called Trump.
"If Trump had called Tsai then it would be very significant but if she called him, it may not suggest a wholesale policy change. China's reaction so far has been calm and muted. It has not blamed Trump but singled out Taiwan."
"It shouldn't be seen as a departure from norms," Pillsbury said. "We should have warmer ties with Taiwan. And it can be done without alienating Beijing. Indeed over the last decade, Taipei has pursued closer relations with the mainland. We too can do both. The zero sum mentality is an old way of thinking."
Damaging breach in protocol?
, who served as President George W. Bush's special assistant for national security affairs, also said the idea of closer US ties with Taiwan was not unprecedented but that Trump's call was a huge breach in protocol.
"The Chinese will go ballistic," Green said. "They will have to, and they will warn the US publicly and will find ways to warn them privately, about this."
Barry Pavel, director of the Brent Scowcroft Center on International Security at the Atlantic Council
said there was a danger that "the Chinese are going to think it was deliberate and that this is the beginning of a hostile policy by the Trump administration, upending the basic geometry of diplomatic relations between the US and China since 1979."
Moving towards an official relationship
Alan Romberg, China expert at the Stimson Center,
said that Beijing -- at a minimum -- would want to strongly reiterate the importance of the US adhering to the One China policy.
"They will also want to be sure that it is not a harbinger of a real change in the policy," Romberg told CNN. But he said he did not think the call would cause a crisis in the US-China relationship.
"At this point Xi Jinping has indicated that he wants a good relationship with the US under President Trump," he said. "Beijing will want to make sure that he acquires the necessary knowledge about this issue."
Richard Bush, the former managing director of the American Institute in Taiwan
, which is the official channel of US interests on the island, said the call wasn't "technically" a breach of the unofficial status of Washington-Taipei relations because Trump isn't yet in the White House.
"China has a couple of options here," he said. "It could choose to be unhappy about this, but not make it a big issue. The other way they could see it is the first step in a kind of probe towards moving towards an official relationship."
He added: China "might calculate that it is better to react vigorously and strongly with the first step rather than wait for the situation to get worse."
Bonnie S. Glaser, the Asia expert at the Center for Strategic and International Studies
, said that the President-elect's call would worry China, but wouldn't necessarily convince Beijing that it was impossible to have a functioning relationship with the Trump administration.
"They will remind the US that obligations are to have an unofficial relationship with Taiwan," Glaser continued. "In private, I expect a little bit of a sharper message that they will deliver to the Trump team."
Indeed in public comments Saturday, the Chinese government appeared to blame Taipei rather than Trump, with Chinese Foreign Minister Wang Yi describing the call as "a shenanigan by the Taiwan side."
"It won't at all change the 'one China' structure that the international community has agreed upon. I don't think it will change the 'one China' policy that US Administrations have adhered to over the years," Wang said on the sidelines of a foreign policy seminar.
"The 'one China' policy is the cornerstone of a healthy China-US relationship. I hope this political foundation won't be disrupted or damaged," Wang said.
China's foreign ministry later issued a statement on the call saying that it had a lodged "a solemn representation with the relevant side in the United States."
"We urge the relevant side in the US to adhere to the 'one China' policy, abide by the pledges in the three joint China-U.S. communiques, and handle issues related to Taiwan carefully and properly to avoid causing unnecessary interference to the overall China-US. relationship," spokesman Geng Shuang said.