Here's the deal ... the music vid for Justin and Quavo's collab, "Intentions," tells the story of a group of women in search of a better life in Los Angeles. The women are all living out of Alexandria House, a shelter for homeless women and homeless women with kids.

The video wraps with a special shout-out to Alexandria House ... Justin and Quavo say they donated $200,000 to the non-profit... and viewers are directed to a link where they can lend a helping hand.

The response has been pretty amazing ... since the video dropped at midnight Thursday, we're told the shelter has received more than $10,000 in donations.

It's pretty cool ... the money is flowing in from all over the world -- Italy, Romania and China, etc. -- and many of the donations are small, as in the $1 and $5 denominations. There've been a few large donations of $1,000 and $5,000, but it's mostly people chipping in what they can afford.

Alexandria House tells us its website is also seeing a huge influx of traffic ... as in, an 800 percent increase in traffic compared to the day before the video dropped.

Justin and Quavo spotlighted 3 women in the video, and we're told some of the funds are going towards their tuition and after-school programs for their kids, plus a one-woman show for the lady who does poetry.

The rest of the money, we're told, will aid the 30 current residents and some 200 former residents ... so they can buy textbooks, furniture for their new homes and even car repairs.

Ah, the power of Bieber and Quavo.