Cruz and O'Rouke last week agreed to three debates.
At Southern Methodist University in Dallas, the two battled over hot-button issues such as immigration, gun rights and trade.
O'Rourke began by praising Cruz's work ethic and his family's sacrifice.
Cruz urged Ford to testify before the Senate Judiciary Committee, of which Cruz is a member, next week. "But I think you are absolutely honest, like Bernie, that you believe in expanding government and higher taxes", Cruz said.
O'Rourke, a US representative from El Paso, called for the FBI to investigate Ford's claims, something that Senate Republicans have resisted, and argued that Kavanaugh's nomination should be rejected.
O'Rourke added that, while he and Cruz disagree on the best moves to make, he has no question that Cruz "wants to do the best for America".
Cruz then likened O'Rourke to former Democratic presidential candidate Bernie Sanders.
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Ford's lawyers said on Tuesday she would testify before the committee only if the FBI first investigates her allegation. The lawyers argue that some senators appear to have already decided that they believe Kavanaugh instead of Ford.
O'Rourke in turn blasted Cruz for supporting massive deportations of illegal immigrants. Mentioning some lower-level judges Mr. O'Rourke said were unsavory yet earned Mr. Cruz's endorsement, Mr. O'Rourke contended Judge Kavanaugh's record with voting rights cases should give marginalized or minority populations in Texas pause. "Imagine the stain on our conscience". Cruz said that O'Rourke was "out of step" with Texans as a liberal.
"It is why some have called this", he concluded, "I think it is an apt description, the new Jim Crow".
Cruz and O'Rourke are facing each other in a surprisingly competitive US Senate race in Texas, a Republican stronghold. Cruz started with a similar response, pointing out that they both have young children and saying, "Every day, when I leave for the campaign trail, it's hard".
Friday night was the first debate for Cruz and O'Rourke. Election Day is November 6. The congressional district where the debate is located is represented by a Republican, Rep. Pete Sessions, but was won by Hillary Clinton by five points in the 2016 election.
Democrats have long dreamed of flipping heavily Hispanic Texas, the country's largest red state, and transforming the national electoral map. If he wins the race, it could help deliver control of the Senate to Democrats.
Sen. Ted Cruz slammed his opponent for the "extreme rhetoric" and defended the integrity of the vast majority of law enforcement officers.