The Indians identified Nikhil Bhatia and Shalini, both students at the Texas A&M University, were rescued from the Lake Bryan, where they had gone swimming, on Saturday.
According to the Bryan police, an officer patrolling the lake was flagged down by a person who said two people swimming in the lake were in distress.
The person who alerted the officer was with the two students, both in their 20s. He had managed to rescue one of them, while the police officer rescued the other one and treated both of them with Cardiopulmonary resuscitation until medical help arrived, the police said.
It was not immediately clear as to why they were swimming in the severe weather.
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India's Consul-General in Houston has been monitoring the two students' medical needs and the situation closely.
According to the Consulate, Nikhil is yet to show signs of improvement, while Shalini showed some improvement today for the first time since she was admitted to the hospital.
Nikhil's mother, Suman Bhatia, has arrived from India. Shalini's brother will be arriving tomorrow, the Consulate said.
Around 13 million people were battling "catastrophic" flooding and torrential rains in the storm-ravaged Texas where Hurricane Harvey has wreaked havoc, turning streets into raging rivers and claiming at least nine lives.
Heavy rain bands were expected to move in over the Houston area overnight, which will continue the catastrophic and life-threatening flash-flood emergency in the area.
At least 200 Indian students stranded at the University of Houston due to the flooding after Hurricane Harvey hit Texas were being evacuated to safer places, authorities have said.
The students were being provided food and other supplies by the Indian-American community in the area.
India's Consul-General in Houston Anupam Ray has been in touch with the students and monitoring the evacuation process.
Ray said members of the Indian graduate students' organisations had reached out to him through Facebook last night. Despite all roads being inundated with water and closed for traffic, Ray personally went to the apartment complex where more than 250 Indian students were stranded.
According to local community leaders, at least 100,000 of Indian-Americans live in and around Houston area have been badly hit by the hurricane.
"We are nervous. We are increasingly getting worried," said Vivek Mehra, who lives in Cypress area of Houston.
On Monday, Pallod received a notice from city authorities to evacuate.
"We have never experienced a situation like this," said Meera Kapoor, who has been living in Houston since 1976.