A 16-year-old suffered a fractured skull and a 13-year-old boy received injuries to his knee in the city's East End.
Detectives believed the three attackers - two men and a woman - may have been involved in a second incident just minutes later.
They forced their way into a property in Whitevale Street, Dennistoun, after knocking the door.
A 47-year-old woman, who lives at the address and is understood to look after one of the boys, was unharmed in the "targeted attack" at 9.55pm on Sunday.
Police are appealing for information about a Ford Mondeo car, in Bellfield Street, which was vandalised just minutes later.
Detective Inspector Ogilvy Ross said: "Shortly after the incident at Whitevale Street, a Ford Mondeo car was vandalised in Bellfield Street, around 10.05pm.
"I'd like to speak to any local people who may have witnessed anyone acting suspiciously around Bellfield Street at that time to contact us."