The vice president said the Class of 2013 and its generation had provided momentum for marriage equality and for a path to citizenship for the 11 million immigrants in the United States illegally.
Graduates gave positive reviews of Biden's speech.
"He was very candid," said Jason Oscar, 22, who graduated with a degree in philosophy, politics, and economics. "He definitely lived up to his reputation of candor."
Biden said America leads the world in innovation because its people challenge orthodoxy. That, he said, does not happen in China.
"Every graduating class faces unique challenges," Biden said.
He talked about problems in his generation, such as the Vietnam War and the assassination of the Rev. Dr. Martin Luther King Jr. He said Penn's Class of 2013 faces the issues of climate change, international terrorism, and pandemic disease.
Aman Goyal, 24, who graduated with a master of science in higher education, said he liked the way Biden compared the two generations. He said the speech gave students a message of hope that better days are ahead.
Biden suggested he was not on campus to give advice.
"I have gained too much wisdom to offer any advice," he said.
Before Biden spoke, Penn president Amy Gutmann awarded him an honorary doctorate of laws.
"Your leadership has shown us that we must not be deterred by the differences which can so often divide us," she said.
Biden joked that getting the honorary degree was much easier than going through the physical and financial duress to earn one the hard way.
Seven others received honorary degrees at the commencement, including Xerox chief executive Ursula M. Burns, who Gutmann said was the first African American woman to lead a Fortune 500 company.
Contact Sulaiman Abdur-Rahman at email@example.com or follow on Twitter @sabdurr.