As reported in later editions of yesterday's Evening Times, 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.
Three attackers - two men and a woman - 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.
However, police are now 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 around that time to contact us."
Police remained tight-lipped about what was used to attack the boys, but confirmed a "blunt weapon" was involved.
The 16-year-old boy today remains in Glasgow Royal Infirmary, where he is receiving treatment for a fractured skull.
Doctors described his condition as "stable".
Witnesses are being urged to come forward and contact detectives. DI Ross, who is leading the inquiry, said "significant inquiries" were continuing.
He added: "I would like to reassure the public and local community that we believe this attack is not random.
"I'd like to speak to anyone who was in the vicinity of Whitevale Street at the time of the incident."
Forensics experts were continuing to examine the scene yesterday.