Renteria previously faced Almanza, who is his sister, in the 2014 runoff election for the same seat.
"I'm ready," Renteria said Tuesday evening at his campaign headquarters at River Street and I-35 in East Austin just north of the Colorado River.
Although Renteria led Almanza by more than 26 points, with 47.95 percent of the vote compared to her 21.80 percent, he lacked the 50 percent needed to avoid a runoff.
"Everyone thought it would be a stretch to get to 50 [percent of the vote], but it's so close it's crazy," Renteria's campaign manager Nic Solorzano said.
Almanza said she was "very pleased" with the results.
"People want to see District 3 going in a different direction," she said, citing the "skyrocketing" cost of housing in the area and the public schools at risk of closure because of low enrollment, which she attributed to families moving out or being displaced, as key issues.
Renteria said his campaign was prepared for a runoff—considering the crowded field, the lengthy ballot, and the challenge of reaching voters who were turning out specifically for U.S. Senate candidate Beto O'Rourke—and that he has experienced running against Almanza.
"I feel good about it," he said of the race ahead.
Almanza, on the other hand, believes her "grassroots" network of supporters would be an advantage in a runoff election.
"A lot of people who came out to vote for Beto [and supported Renteria] won't be returning [to the polls]," she said. "So for us, it's a plus."
Renteria and Almanza were two of six candidates running for the seat. EMT Jessica Cohen came in third, with 8.94 percent of the vote, ahead of United Way Chief Information Officer Amit Motwani, with 7.75 percent; real estate broker James Valdez, with 6.84 percent; and restaurant worker Justin Jacobson, with 6.32 percent.
For more information on this race, see our coverage of the early voting results.