Scientists at the space agency were due to launch the probe yesterday - but it was called off due to "gaseous helium red pressure alarm".
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.
The heat shield is built to withstand radiation equivalent to up to about 500 times the Sun's radiation on Earth.
The project, with a $1.5 billion price tag, is the first major mission under NASA's Living With a Star program.
Powered by a United Launch Alliance Delta IV Heavy rocket, the car-sized probe will travel millions of miles to reach the sun's corona, or outer atmosphere.
Experts say a worst-case scenario could cost up to two trillion dollars in the first year alone and take a decade to fully recover from.
"The unique requirements of this mission made the Delta IV Heavy the ideal launch vehicle to deliver Parker Solar Probe into orbit with the highest precision", said Gary Wentz, ULA vice president of Government and Commercial Programs.More news: Wolves agree fee with Middlesbrough for Adama Traore
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Even in a region where temperatures can reach more than a million degrees Fahrenheit, the sunlight is expected to heat the shield to just around 2,500 degrees Fahrenheit (1,371 degrees Celsius).
If all works as planned, the inside of the spacecraft should stay at just 85 degrees Fahrenheit. The probe is set to make 24 passes through the corona collecting data.
"Fly baby girl, fly!" project scientist Nicola Fox of Johns Hopkins University said in a tweet right before liftoff.
"We are ready. We have the ideal payload". A key question that the probe seeks to answer is how solar wind is accelerated, and for the first time it will be able to look for answers at the source of solar wind itself.
It was the first rocket launch ever witnessed by Parker, professor emeritus at the University of Chicago. "We're in for some learning over the next several years", he said as he watched the lift-off.
Speaking after the launch, the 91-year-old told NASA TV: "It's a whole new phase and it's going to be fascinating throughout".
Zurbuchen also described the probe as one of NASA's most "strategically important" missions.
The delicate instrument comes equipped with an array of instruments and tools which will scan the Sun for solar winds and magnetic fields.
When it nears the Sun, the probe will travel rapidly enough to go from NY to Tokyo in one minute - some 430,000 miles per hour, making it the fastest human-made object.