Drake and The Game are teaming up to help cover funeral costs for 6 people -- including 5 young siblings -- who died in a tragic house fire in Ohio ... even though the rappers didn't know the victims.

The Game got the ball rolling after learning about Anna Angel -- who was working her shift at Burger King when a fire consumed her home while her 5 young children and her boyfriend were trapped inside. There were no survivors.

Game Instagram'd about the tragedy ... saying, "I can deal with a lot of things but people losing their children is something that kills me every time."

The Game -- who recently pledged to donate $1 million dollars to people in need as part of his Robin Hood project -- says he was on the phone with Drake when he read about the woman's loss ... and they each agreed to donate $10,000 to help Anna cover the burial costs.

Drake later posted about the situation ... saying, "What [The Game] is doing will never be forgotten. Honored to be able to help people along side my brother."

In addition to their $20K ... the producers of Game'sTV show, "Marrying the Game" also pitched in $2,500.