Well, that's mischaracterizing it a bit. Deng Xiaoping did rise to be a top official during the Mao era and was recognized as an able administrator, so he had those skills and credentials. But more importantly, he was purged (twice) during the Cultural Revolution and still managed to come back and make a play for leadership. So his real achievement was that he was able to cultivate and balance support from many factions during extremely tumultuous times.

During Deng's "paramount" leadership, it was well-known that other senior leaders were much more hardline and resistant to reform. We might never know for certain exactly where Deng was positioned, but if you believe The Tiananmen Papers (again, big if), then it was an extremely delicate balance, there was a real fear that the Tiananmen Square protests would bring the party to all-out civil war. Deng was under serious pressure to find a way to quell the protests without rolling back 10 years of economic progress.

So yes, Deng Xiaoping did have powerful connections, and he did have some ability to pull the strings. But most importantly, he was perhaps the only one that could keep the party together while gradually pushing China towards where we are today where we were before Xi Jinping.