Authorities said the stabbing happened during an early morning confrontation Friday at their home in the 4400 block of 17th Street in Bacliff.
Vazquez left the scene immediately after the stabbing, officials said. Galveston County Sheriff's Office investigators worked non-stop to apprehend him.
Investigators learned late Saturday that Vazquez told friends of an alleged family emergency. He apparently told them he needed help returning home.
Friends helped him reach Houston, where he is believed to have boarded a bus bound for Mexico.
Working in cooperation with Immigrations and Customs Enforcement agents and Austin police, Vasquez was taken into custody around 10:45pm Saturday at a bus station in Austin.
Vazquez was returned to the Galveston County Jail where he remained Sunday under a $150,000 bond.
GCSO detectives are continuing their investigation, talking with other witnesses and reviewing evidence in their efforts to finalize the case.