Have humans evolved to live longer?
Yes and no.

According to this paper, great apes and our ancestors had a life expectancy at birth of about 13 years (chimpanzees). Over a few million years of evolution, human life expectancy rose to >30 years in the 18th century. Industrialization and improved nutrition, hygiene and medicine resulted in a jump to >60 and now around 80 years in developed countries in just 200 years. The paper compares data from Sweden, but if you look at the data from gapminder.org, you see that this trend holds true for all nations (especially developing countries like India and China, who doubled their life expectancy in just 50 years).

So, while humans have evolved to live longer (as you asked in the title), due to a lower mortality and resulting increase in the age of maturity as well as the likely benefit of "grandmothers" (older, infertile females helping to feed their grandchildren) (discussed in this source), the recent increase in life expectancy in just a few generations is unlikely due to evolution.

While humans are still evolving, we have reduced the selective pressure. There is no benefit to the survival of the offspring when we live past 80-100 years. And comparing countries with lower standards in hygiene and medicine (I totally recommend playing with the gapminder tools), their life expectancy was still pretty low in recent years, only increasing with access to clean water, food and medicine. Comments on extending the lifespan usually refer to medical interventions to cope with the effects of aging.