The debate at Dallas' Southern Methodist University also saw Cruz criticize O'Rourke's past support for legalizing marijuana, evoking his older half-sister, Miriam, who died of a drug overdose.
O'Rourke called for the FBI to investigate Ford's claims, something that Senate Republicans have resisted, and argued that Kavanaugh's nomination should be rejected.
Mr. O'Rourke claimed things like "universal background checks" would make schools and other places "demonstrably safer", before chiding Mr. Cruz that "thoughts and prayers are not going to cut it". He noted that O'Rourke has expressed an openness toward abolishing the U.S. Immigration and Customs Enforcement Agency and impeaching President Donald Trump.
"We're talking about criminal justice reform", O'Rourke said to the audience, "let's talk about where this problem started". "Imagine the stain on our conscience".
Such work would prove hard, Mr. Cruz said, given Mr. O'Rourke "has never talked to the president and wants to vote for impeachment". O'Rourke shouted out his "uncle Raymond", who taught him to shoot a firearm and was in law enforcement. The two will debate twice more before Election Day. Democrats need to win a net total of two additional seats to take the Senate and 23 to assume the majority in the House.
Cruz drew the ire of many Texas conservatives for refusing to endorse Trump during the 2016 Republican National Convention.
If Democrats win control of either chamber, much of Trump's agenda would be stymied and his administration would be subjected to greater scrutiny. A recent poll conducted by Quinnipiac University showed Cruz leading O'Rourke by nine points. Democrats have not elected a Democrat to the Senate in three decades.
The UVA poll also revealed that Hispanic voters supported O'Rourke over Cruz by a ratio of about 2-to-1.