The launch was called off at the last minute on Saturday after a gaseous helium pressure red alarm emerged that the scientists did not have enough time to troubleshoot.
The probe will dip inside this tenuous atmosphere, sampling conditions, and getting to just 6.16 million km (3.83 million miles) from the Sun's broiling "surface".
From Earth, it is 93 million miles (150 million kilometers) to the sun, and the Parker probe will be within 4 percent of that distance at its closest.
Even though it will repeatedly fly through the corona, Parker will not experience such extreme temperatures because the ionized gas making up the outer atmosphere is so tenuous.
"We've been inside the orbit of Mercury and done unbelievable things, but until you go and touch the sun, you can't answer these questions", Nicola Fox, mission project scientist, told CNN. She urged it to "go touch the sun!"
Greeting the launch - on the back of a mammoth Delta-IV Heavy rocket - NASA tweeted: "3-2-1... and we have liftoff of Parker #SolarProbe atop @ULAlaunch's #DeltaIV Heavy rocket".
However the technology to make the spacecraft small and light enough to travel at incredible speeds - while surviving the sun's punishing environment and the extreme changes in temperature - are only now possible.
The spacecraft will face heat and radiation "like no spacecraft before it", the agency said.
Protected by a revolutionary new heat shield, the spacecraft will fly past Venus in October, setting up its first solar encounter in November.
The spellbinding footage shows Parker's engines ignite propelling the probe towards the sun to start its seven-year-long mission to explore the Sun. With a communication lag time of 16 minutes, the spacecraft must fend for itself at the sun.
The probe is the first NASA spacecraft with a living namesake.
The $1.5bn (£1.17bn) project is created to give scientists a better understanding of solar wind and geomagnetic storms that risk wreaking chaos on Earth by knocking out the power grid.
In particular, it is hoped to give scientists a greater understanding of solar wind storms that have the potential to knock out the power on Earth. "Why has it taken us 60 years?"
No wonder scientists consider it the coolest, hottest mission under the sun, and what better day to launch to the sun than Sunday as NASA noted.
More knowledge of solar wind and space storms will also help protect future deep space explorers as they journey toward the Moon or Mars.