The protesters chanted 'Refugees are welcome here' during the blockade in Pollokshields.
Scotland's First Minister Nicola Sturgeon, who wants to wrest immigration powers from the United Kingdom government, welcomed the police force's actions and blamed the British government for what she called a "dangerous situation".
Video footage showed the two men emerging from the back of a van belonging to Britain's interior ministry, which sets immigration rules for the whole United Kingdom.
After a stand-off lasting several hours, a crowd of onlookers clapped and cheered as one of the men waved and police officers made space for them to walk free, pending further investigation.
British immigration officers had originally asked local police for assistance after a crowd gathered to block them.