In the footage Mrs Clinton is seen closing her eyes as Rev Dr William Shillady gives the benediction minutes after she accepted the Democratic nomination to run for president.
She can be seen wiping a tear from her eye towards the end.
Running mate Tim Kaine, a devout Catholic, and her husband Bill are also seen closing their eyes in prayer.
Rev Dr Shillady is a family friend of the Clintons and was their minister at the local Methodist Church in New York.
"Let's pray with Bill," Mrs Clinton said.
Mr Clinton can be heard saying: "This is the guy that married Chelsea [Mr Clinton's daughter] and Mark."
Reciting the prayer, the pastor said: "Lord God, give us the courage to leave this place with determination and fortitude to move onward and upward to become a better nation, one that can solve our many problems together, not apart.
"Help all of the world to see our nation as a shining lamp on a hill."
