A Chinese music student has been executed after he stabbed a woman to death immediately after hitting her with his car because he was worried that the "peasant woman would be hard to deal with".

The swift execution of Yao Jiaxin, 21, who studied at the prestigious Xi'an Conservatory of Music, comes after a public outpouring of anger at a case that was widely perceived as an example of the Chinese élite's assumption of impunity. It followed several cases of well-connected drivers escaping censure over dangerous driving. Yao – who was not from an especially rich or powerful family – ran over Zhang Miao, a 26-year-old waitress, in his Chevrolet Cruze as she cycled home from work. Fearing Zhang, who has a child, would remember his number plate and report him to the police, he stabbed her eight times.

This week, Yao was executed for the murder in the capital of north-west China's Shaanxi province. The Xi'an Intermediate People's Court handed down the death sentence for intentional killing on 22 April. Yao's appeal was rejected by the Shaanxi Provincial Higher People's Court on 20 May.

Download the new Independent Premium app Sharing the full story, not just the headlines

As part of new efforts to reduce the number of death sentences meted out, the Supreme People's Court reviews every death sentence before execution. "Yao, after running into the victim, stabbed the victim's chest, stomach and back several times until she died. His motive was extremely despicable, his actions extremely cruel and the consequences extremely severe," said a statement from the court as quoted by the Xinhua news agency.

The case has caused a major sensation on Sina Weibo, the Chinese equivalent of the banned Twitter, with more than a million micro-blog postings mentioning the execution. The Communist Party is keenly aware that the biggest cause of social unrest, and the most serious threat to its single-party rule, is a feeling among the common people that the "second generation rich", China's army of newly wealthy, abuse their privileged positions at the expense of the peasantry.

This kind of abuse of power can help fuel what the government calls "mass incidents", including petitions, demonstrations and strikes, both peaceful and violent. There were 280,000 such incidents in 2010, a steep rise from 87,000 in 2005, according to the figures from the Ministry of Public Security.

Late last year, Li Qiming, who was drunk, drove his black Volkswagen Magotan into two rollerblading students outside Hebei University, killing one and injuring the other. When he was intercepted by security guards and students, he said, "Sue me if you dare. My dad is Li Gang", referring to his local police chief father. He escaped execution, but was jailed for six years and ordered to pay compensation.

Yao's father, Yao Qingwei, apologised on his micro-blog to Ms Zhang's family and "all Chinese people" for what his son had done.