You ask what innovations caused the PRC to outlive the USSR, but the answer is as much about what innovations caused the USSR to collapse. I'll however start with a quotation about what isn't the issue, from Melvin Goodman. Head of Office for Soviet Affairs CIA 1976-87.
I think probably one of the greatest myths in America, in the
political discourse now, right now, is that actions of the American
government were responsible for the collapse of the Soviet Union. The
Soviet Union collapsed like a house of cards because it was a house of
cards. It rotted away from within. The economy was rotten, the
political process was rotten, they had developed a central government
that was no longer believed by people outside of Moscow, there was
total cynicism throughout the Soviet system of governance, there was
no real civil society. But the Reagan Administration and their—the
minions of the Reagan Administration, will tell you that Afghanistan
led to the collapse of the Soviet Union itself—the collapse of the
Berlin Wall in 1989, the collapse of the East European empire. We were
saying that this was entirely fanciful. And the United States missed
all of this, because they believed their own myths and their own
fanciful notions. They had become their own victims of their own lies.
So what actually happened? We need to go back to 1953... perhaps as far back as 1922. Lenin hoped that Bolshevik victory would inspire revolutions across Europe. But his gamble failed, and with it the prospect of global communist revolution faded. Lenin believed that a communist society could not compete with a capitalist one, and without global revolution a change of strategy was required.
In 1922 Lenin initiated the New Economic Policy, or "state capitalism". The USSR would liberalise its economy; allowing private enterprise and operating state industries for profit. Additionally he proposed Socialism in One Country; another compromise with the failure of global revolution. Lenin died in 1924 and Stalin came to power. Stalin had been initially supportive of the NEP, but he changed his mind, favouring rapid collectivist industrialisation over gradual economic liberalisation. Stalin however did not reject Socialism in One Country, this became a central pillar of his own ideology.
Stalin's Russia became the standard model for communism, and his political and economic policies were copied by Mao's China and Kim Ill Sung's North Korea. The most important part of Stalinism was the cult of personality. Stalin's Russia and Mao's China both experienced dire famines resulting from the poor management of collectivised agriculture. But this wouldn't be a problem, because it was unthinkable that the leader was wrong. Even more unthinkable that one would complain about it. Stalin's brutality kept the Soviet people in line, and meant that their happiness, prosperity, and even their lives were an irrelevance.
In 1953 Stalin died, and his successor Nikita Khrushchev began de-Stalinisation. This aimed the USSR towards political liberalisation, culminating in Mikhail Gorbachev's Glasnost and Perestroika reforms come 1986. The PRC and North Korea however chose another path. Mao's Cultural Revolution, which lasted 1966-76, was a particularly bloody and horrible moment in Chinese history. One seemingly inspired by Stalin's Great Purge of 1936-8.
Mao died in 1976, and was effectively succeeded by Deng Xiaoping in 1978. Unlike the Soviets, the Chinese did not get rid of their late leader's personality cult. Importantly, Deng's reforms (Deng Xiaoping Theory) were said not to reject, but to adapt Marxist-Leninism and Maoism. Even when these policies were polar opposites to what had come before. Perhaps his most famous phrase is:
"It doesn't matter whether a cat is white or black, as long as it
This sentiment should seem familiar, as what Deng did was to follow Lenin's New Economic Plan. Today the PRC's largest corporations are state owned heavy industry operating for profit, and free enterprise is a cornerstone of Communist party strategy.
In 1968 the Czechoslovakian Communist party attempted to promote political and economic liberalisation; Socialism with a Human Face. The reforms were put down by a Soviet invasion, in what would become known as the Prague Spring. Years later, when Gorbachev was asked what the difference was between his reforms, and the reforms proposed by the Czechoslovakians, he replied "Nineteen years."
The main difference between the USSR and the PRC in 1989 was the degree of authoritarianism which was accepted by the people and enforced by the party. The Tiananmen Square Protests went the way of the Prague Spring as the Communist party feared they were about to lose control. There's intriguing parallels between the Tiananmen Square Protests and the Prague Spring. The latter happened 15 years after Stalin's death, and the former happened 13 years after Mao's death. This implies that the USSR and PRC were in a similar place psychologically in these respective moments.
In 1989 the Chinese Communist party had yielded little political control over their society. Contrast that with it being 51 years since Stalin's Great Purge, and by then the USSR had gradually become a far more liberal society, far more willing to criticise authority and far less willing to put down dissent with violence.
The PRC and DPRK both endure, not because of economic factors given North Korea's poverty, but because of unrepentant authoritarianism. Without de-Stalinisation the USSR would likely still be with us, because it would still have the brutality required to enforce its existence.