9/20 5:07 PM PT -- The LAPD has now released a video of the crime going down ... showing one of the suspects smashing in the front door with several kicks. Cops are asking for help in identifying the men involved.

7:07 PM PT -- LAPD has just released a photo of one of the suspects, captured by Puig's home security system.

Cops also provided further details, saying the 3 men -- 2 of which are believed to be black males in their early to mid-20s with slim builds -- ransacked Puig's home then located a safe in the second-floor master bedroom. They allegedly dragged it down the stairs through the living room, but fled without it ... leaving it in the doorway.

LAPD claims the suspects caused about $10k in damages. They have no description so far of the third suspect, who was the driver.

The 3 suspects are believed to be the same burglars who hit Puig's house on August 30.

Yasiel Puig really needs to do something about his home security, 'cause he was burglarized yet again -- the 4TH TIME he's been hit ... TMZ Sports has learned.

Law enforcement sources tell us cops were called to Puig's San Fernando Valley home Tuesday night around 8 PM after one of the Dodger's assistants got a security alert on his phone, which showed 3 men leaving Puig's property.

Yasiel has a security camera set up that captures motion, and it automatically sends the video to a cell phone programmed to receive it. When Yasiel's associate saw the footage, he immediately called police ... but the bad guys had already fled.

We're told the men broke in through the back door ... smashing it open. It's unclear at this point if anything was taken.

Yasiel wasn't seen celebrating with his team at Dodger Stadium Tuesday night after their walk-off win against the Rockies, but the game went late ... and he presumably left when he got called about the break-in.

If you're keeping track ... Yasiel's been burglarized now a total of 4 times. He initially got hit last spring while he was away for spring training, then again during the World Series last year ... and a third time just last month. Our sources say cops aren't sure if the burglaries are connected, but it's clear someone is keeping track of Yasiel's work schedule, 'cause he's never been home.

Time to get a watchdog or something, Yas. That's our advice.