Devlin said a fire crew was able to help her and her family get out safely.
"I just thank God we're alive," she said. "I haven't cried any — I've just been panicked."
Former President George W. Bush and his wife, Laura, live in the area. A representative of the family told NBC News that the Bushes were safe and that they were praying for their neighbors.
Texas Gov. Greg Abbott tweeted his support for those affected, saying: "We are sending prayers. We are also sending the Texas Division of Emergency Management to provide assistance. Stay safe Texans."
Dallas Stars player Tyler Seguin tweeted Monday morning he was safe after a local reporter shared images of a house badly damaged in the tornado.
"Luckily this is my house for sale and I have moved into a new one," Seguin said. "I just left the area and it is an extremely sad sight to see. Prayers to everyone affected by the tornado."
Dallas fire officials told NBC News that an unspecified structure collapsed near the area where the tornado touched down. They said as many seven people were able to make it out of the structure safely but that a search and rescue team was on the scene to look for other people.
Authorities didn't identify the structure, but NBC Dallas-Fort Worth showed a flooring company building in the immediate area with its front half crumpled in a heap.
Fire officials said they were also responding to multiple calls for people who had been injured by broken glass.
Police officers in Garland, a community northeast of Dallas, where a tornado warning was also issued, reported major structural damage in a residential area, but said there were no substantial injuries.
Several schools sustained "significant damage" and will be closed Monday, the Dallas Independent School District said.
Oncor Corp., the main electric provider for the Dallas area, reported that more than 70,000 customers still remained without power in Dallas county at 5:30 a.m. (6:30 a.m. ET).
The company said it has experienced significant damage to power lines and it was working to restore power as quickly as possible.
The tornado didn't affect the Dallas Cowboys' game on Sunday night against the Philadelphia Eagles in Arlington, west of Dallas.
Meanwhile, in far southwest Tennessee, a twister forced temporary evacuation of at least one terminal at Memphis International Airport on Monday morning.
The airport retweeted a photo posted by a traveler of an empty gate area and ticketing area. The airport said "minor damage was sustained" but that "normal operations have resumed."
CORRECTION (Oct. 21, 2019, 9 a.m. ET): An earlier version of this article misspelled the last name of a Dallas Stars player. He is Tyler Seguin, not Seduin.