Sen. Kamala Harris outshined all of her 19 rivals in the first Democratic presidential debates, a longtime Republican pollster told CNBC on Friday.

"She owned the stage, and Joe Biden should have known it was coming," Frank Luntz said in a "Squawk Box" interview the morning after the second round of debates by Democratic presidential hopefuls.

Harris, a first-term U.S. senator and former California attorney general, came out swinging Thursday night, with pointed attacks on frontrunner Joe Biden. She called out the 76-year-old former vice president on race, saying the way he recently described his past working relationship with two segregationist lawmakers was "hurtful."

The 54-year-old Harris, if elected, would be the second biracial president. Former President Barack Obama was the first. Harris' parents were both immigrants — her father from Jamaica and her mother from India. They met as graduate students at the University of California, Berkeley.

At Thursday night's debate, Harris also accused Biden of opposing busing, which Biden disputed.

"There was a little girl in California who was part of the second class to integrate her public schools, and she was bused to school every day, and that little girl was me," Harris said.

Biden called Harris' attack "a mischaracterization of my position across the board," and launched into a fiery defense of his record on race. "I did not praise racists."