The series opener takes place at 6 p.m.at Southern Methodist University, with the next two are scheduled for Sunday, Sept. 30 in Houston and Tuesday, Oct. 16, in San Antonio.
The pair will square off again next weekend in Cruz's hometown of Houston, and a third and final debate is set for San Antonio three weeks before the November 6 election. A recent poll conducted by Quinnipiac University showed Cruz leading O'Rourke by nine points.
They differed on gun rights - with O'Rourke arguing for some limits on gun rights and saying that "thoughts and prayers are just not going to cut it", and Cruz insisting that "gun control is not the answer".
Cruz shot back that he became a Republican in part because of the party's support for civil rights, while Democrats in the South supported Jim Crow laws. "I think this is by design for the O'Rourke campaign, they've wanted to create that visual sense that they are making inroads in hostile territory", Wilson added. "Imagine the cost", O'Rourke said. In Mr. Cruz's case, the senator showcased a masterful command of nearly every topic, while Mr. O'Rourke unfailingly managed to take any issue and tie it to a specific individual he has met while crisscrossing Texas.
President Trump will visit Texas in October to stump for Cruz.
O'Rourke replied: "True to form".
O'Rourke, though, faulted Cruz for not opposing Trump more and said the president undermines American democratic institutions.
"I've got a responsibility, which is to fight for everybody here and every person in this state", he said. He then suggested he wants the woman who accused him of sexual assault to testify "respectfully" before the Senate Judiciary Committee.
"We need a junior senator who will stand up to this president", O'Rourke said.
O'Rourke first challenged Cruz to six debates in May, and while Cruz maintained he was open to debating his opponent, he did not formally respond until July.
Cruz recalled meeting with students and teachers from the school.