The Pakistani men, aged 24 and 28, now face questioning over suspected immigration offences.
It came during a crackdown on crime by around 50 police officers in Govanhill.
From 7.30am yesterday, officers of Strathclyde Police Force began searching cars across the area looking for people involved in illegal activity.
Officers worked with staff from the UK Border Agency and the Vehicle and Operator Services Agency.
A total of 53 vehicles were stopped and searched and a 57-year-old man was held in connection with traffic offences. The suspected illegal immigrants were in a car in Victoria Road.
Police also identified six vehicles which will later be seized if their serious faults are not fixed.
The day of action was part of Operation Myriad, a sustained, six-month long attack on all levels of crime in the whole Strathclyde force area.This month the focus is on G Division, which covers the South Side and East Renfrewshire.
Chief Inspector Mark Hargreaves, area commander for Pollokshields and South Side Central, said his teams were also looking for metal thieves.
He said: "We have a lot of metal theft in this area while the UKBA were looking for illegal immigrants."
Mr Hargreaves said his team was tackling crime, "from a number of different angles" and added: "People who are in cars that aren't legitimate are generally involved in other criminality."
He added: "Yesterday was our day of action. However, we'll be continuing to target specific areas of crime."
During the clampdown a 16-year-old male was arrested over a housebreaking.
Officers also swooped on properties in a series of drug raids while people with outstanding warrants for serious offences were also in their sights.