"They marked their trail with fresh leaves, which was really kind of clever," Commander Frank Urias with Austin/Travis County EMS told CBS affiliate KEYE. "The proverbial trail of breadcrumbs."
The two women and one man, found in a 500-foot-long crawl space about the width of a sewer pipe, waited there knowing search teams would arrive, said Lt. Matt Cox of the Austin Fire Department.
"They did everything right," Cox said. "They came out safe and sound, and they're going to school tomorrow."
The University of Texas students emerged from Airman's Cave after 30 long, dark and increasingly frightening hours. The three were covered in mud, hungry and thirsty, but - remarkably - uninjured … and just as remarkably, in high spirits.
"We're all great," one said. "The cave is hard, it's demanding, but, um, it was fun."
They had left a trail of leaves during their exploration so crews could find them if they got into trouble, Cox said.
"We were just thinking it's a good idea," Jeff Brown, one of the rescued students, said. "If someone's coming it's a good way to find someone."
The group went into Airman's Cave on Saturday morning and told friends to call for help if they weren't back by midnight, Cox said.
"They accounted for something like this happening," Cox said.
One student said, "Even when we did get lost we totally kept our cool. Nobody panicked anywhere in the cave."
Jarvis Brown, whose 20-year-old son Jeff was among those in the cave, said his son had been cave exploring before.
"We're very elated, for sure, and thankful that God protected them," said Brown, of San Antonio.
Jeff's mother Lyn Brown was also relieved, and proud of her son.
"He's an adventure seeker. He loves being outside. He loves anything new. He always wants to conquer something and he researches it, and that's what he likes to do."
The narrow, 12,000-foot long cave is one of the most difficult for cave explorers in Austin and an easy place to become disoriented, authorities said.
The "keyhole" entrance to the cave, which is in a greenbelt area about five miles south of downtown Austin, is less than 18 inches across. Many places in the cave can be accessed only by crawling, authorities said.
During the search, crews found water bottles and cell phones apparently left behind by the students. Rescuers had left food, water and medical supplies throughout the cave.
Officials said 14 people were searching, five of them private citizens.
CBS News correspondent Hari Screenivasan reports that, despite their experience, all three students say they'll be back caving - very soon.