The actor -- best known for the TV shows "Westworld" and "Kingdom" -- appeared on doorbell camera footage from his neighbors' house Sunday night when he rushed to their aid after a man allegedly pushed his way into the Hancock Park home.

Check out the clip obtained by KCAL News ... Jonathan has a bag slung over his shoulder and walks quickly into the house while screams can be heard from inside. Video from the street later shows JT running out with one of the kids in his arms.

The homeowner -- who spoke on the condition of anonymity -- says Jonathan's a hyper-vigilant force in the neighborhood ... adding he's pretty sure the actor tracked the individual for a while and called the cops even before he could.

We broke the story ... Tucker called 911 Sunday to report a suspicious man walking around the neighborhood, banging on doors and talking to himself. A clip from the camera at the home shows him seemingly pushing his way inside.

We're told Jon found the little girl he's seen carrying in the video before coming across the mother and her baby. He explained the situation and led them out of the house before police arrived.

Cops say they went into the home and allegedly found the man hiding in a closet. Law enforcement sources tell us the man was put on a 5150 psychiatric hold.