The California senator called Biden by his first name as she smiled in return.
Harris is one of the former vice president's top rivals and sharpest critics. Biden is a 76-year-old white man. Harris is a 54-year-old black woman.
Their generational and racial differences were on display last month in the first debate, when Harris hammered Biden for his opposition to federal court-ordered busing in the 1970s as a way to desegregate public schools like Harris's elementary school in California.
Biden has promised to defend his record more forcefully in this debate.