Before the Second Sino-Japanese War, Chiang Kai-Shek was able to actively and successfully pursue and annihilate CCP armies or uprisings. During the War, this all stopped for obvious reasons but after the war was over, the only land still in firm CCP control was Shaanxi (to the best of my knowledge, correct me if I'm wrong) and the communists were able to so suddenly (it seems) turn the tide and crush the Nationalists on multiple fronts. Why did the tide turn so much post-WW2 even though both sides were subjected to attack by the Japanese?
There are a lot of factors that came together to allow the CCP defeat the Nationalists. It's a complicated question and I may miss or misunderstand some so please bear with me.
First was that after WW2, the Nationalists were broke. They had spent all of their money to arm themselves and the other factions so they could unite against the Japanese invaders. They had to rely on support from the West to continue fighting the Communists.
Second, the Nationalist Army was huge, 600-700,000 men. They were mostly conscripted from the rural peasantry and the urban workers, sometimes kidnapped. This gave them less will to fight than the idealogically driven CCP. There were some factions in the CCP, broken mainly along Trotskyist and Stalinist lines, but they were still able to hold together due to the base support of Communism.
After a while, the Nationalists lost the support of the West and began to run out of money and, more importantly rice. This lead to mutiny and desertions among the peasant soldiers. When you add in the corruption that was rife among the Nationalist Officers and Elite, the situation became worse. They stopped paying the soldiers and cut down the rice ration. A lot of deserters then joined the CCP.
Russia moved troops into Manchuria, which kept the Nationalists from getting the left over Japanese weapons and supplies. Without this action by the Russians, the Nationalists would have gotten enough material to extend their fight and probably defeat the CCP in the end.
In addition to the takeover of Manchuria, the Russians began to support Mao's troops with money, modern armaments and food. This strengthened the CCP and allowed some military successes. This brought new recruits from the liberated cities and rural areas that were tired of the corruption in the Nationalists government.
There are more factors to be sure, but this is kind of a glossed over basic explanation.