Air carrier Captain reported a critical ground conflict with a vehicle which resulted in the flight crew taking evasive action.

Narrative

Last night Aircraft X was taxiing into their gate at ZZZ. After seeing the ready ground crew; wands; clearing the silhouette and area around the turn; I began to turn right. As I did; my FO checked our right blind spot behind the cockpit window line (which required him to lean forward and look back). It was at that moment; when I was about 60-45 degrees off the parking bay center line that my FO spotted the oncoming tug (used for moving cans around the ramp) pulling the line of empty dolly's. The tug was crossing right to left at a rapid pace. The FO determined that the tug had no intentions of stopping and before I could see the threat; he vocalized it and directed me to immediately stop. I was able to stop the aircraft without incident but it was close enough that the tug passed under the nose out of sight of my vision until the tug passed to the left. We reassessed the situation after the vehicle cleared and again went through the process of clearing the space and slowly continued into the parking bay. The aircraft was shut down and no damage was done. Had my FO not checked behind us in the turn; the ability for me to see the tug (which I don't think had lights on) would never have presented itself. The FO in my opinion saved us from a very close call or worse.To the tug drivers credit; he did not drive off but pulled into the area next to the parking bay and came over to apologize and debrief what happened.The driver was respectful; polite and very very remorseful. He did not blame anyone but his own actions and profusely apologized. I asked him what happened and he said he just lost track of his surrounds and didn't see us. I asked him if he was on the phone or listening to music but he said he wasn't. I believe him. I asked him if everything else was good with him and had he slept well the day prior. He admitted that he had not slept well and was tired. He looked exhausted and cold. I asked him how to prevent the event in the future and he said he needed to be more aware of his surroundings. I gave him some tips for clearing for aircraft when approaching parking bays and mentioned that lack of sleep can cause fatigue and accidents.I wanted to give my first hand immediate impressions of what must have been a very scary and stressful situation for the young man and how he handled it.My FO deserves recognition so I would ask how I can help facilitate that. I have considered things myself from inside the cockpit and do not see what we would have changed to avoid the near miss other than what I discussed and debriefed with the driver. I will continue to ask my FOs to always check our blind spot when turning into them. Cause: Fatigued ground crews. If the tempo remains this high between aircrew and ground crews there will be an accident.