Kirk, the first black mayor of Dallas, held a thin lead over Morales, the 1996 Democratic Senate nominee, in nearly complete returns from the Texas primary Wednesday, but neither candidate had the 50 percent necessary to avoid the runoff.
With 99 percent of the vote counted, Kirk had received 33.3 percent, Morales 32.9 percent and Rep. Ken Bentsen, D-Texas, trailed with 26.6 percent. Bentsen, the nephew former Texas Sen. Lloyd Bentsen, had not conceded early Wednesday.
After a night of lead changes in the three-way battle, Kirk told his supporters early Wednesday he was in the runoff with Morales.
"We want to win the runoff, and we want to win in November," he said. "Tomorrow morning, I've got to go back to work, and we've got to do it again."
Kirk, 47, the first black mayor of a major Texas city, hopes to become the state's first black senator. The Dallas attorney served as Texas secretary of state during the administration of Gov. Ann Richards, who has worked in his campaign.
Morales, 52, is remembered from his 1996 Senate race when he drove a little white pickup truck across the state in a populist campaign that drew thousands of voters. He defeated an incumbent congressman in the primary and drew 45 percent of the vote in a losing challenge to Sen. Phil Gramm, R-Texas.
Morales, heavily outspent by his opponents, said his second bid for the Senate was vindicated by Tuesday's vote. The geography teacher from Crandall, just southwest of Dallas, led the field most of the evening.
"Based on the thousands of people who urged me to run, I felt the support was out there," he said.
The stage for the Senate race was set when Gramm announced last year he was retiring from the Senate. There has not been an open Senate seat in Texas in nearly a decade.
On the Republican side, Attorney General John Cornyn easily won his party's nomination over four political unknowns. He has a $2.5 million campaign war chest ready for the general election, far more than either of his possible opponents.
President George W. Bush has stayed out of the election in his home state so far, but he is expected to attend Texas fund-raisers for both Cornyn and Republican Gov. Rick Perry, who faces Democrat Tony Sanchez, a multimillionaire businessman from Laredo.