At one point it stayed inside the corona for five hours, travelling at 62 miles (100 km) per second.
Nasa said the corona turned out to be dustier than expected.
Studying it would help scientists better understand the solar wind and how it was projected out into space, and solar disturbances that can interfere with Earth.
A Nasa spokesman said: “Just as landing on the Moon allowed scientists to understand how it was formed, touching the very stuff the Sun is made of will help uncover critical information about our closest star, and its influence on the solar system.”
Parker discovered that the edge of the corona, which is called the Alfvén critical surface, is not a smooth sphere around the sun, but has areas of spikes and valleys.
It also went through a previously observed area called a “pseudostreamer” where the solar atmosphere was quiet like the eye of a storm.