B737 Captain reported a baggage tug turned close enough to the nose of the aircraft that the pilot had to brake to prevent a collision which resulted in a critical ground conflict.

Narrative

During our westbound taxi out from the ZZZ south ramp just prior to spot XX; a Company X baggage tug (tug only-no carts in tow) turned in front of the aircraft while it was still on the vehicle service road that links X gates with Y gates; requiring a brake application from the flight crew to prevent a collision/overrun of the tug.The roadway was located approximately between gates XXX and YY that runs north to south. As the vehicle turned it proceeded southbound onto that road right in front of our forward right corner of the aircraft. Earlier as we taxied westbound towards spot XX on the taxi line; the tug was observed also westbound along side but slightly ahead of us on the northern access road (closer to the X gates that parallels running east to west) prior to reaching the southbound service road- where the tug took a left without stopping southbound which placed it close to the nose of the aircraft. Both myself and the FO noticed the tug swing left and start to go in front of us; at which point I applied the brakes to prevent a collision. As the tug made the turn in front of the aircraft it was close enough that portions of the vehicle were on the flight deck dashboard itself/close view proximity; and that the flight deck deck crew could see detailed and distinguishing features of the tug and the 1 person wearing an orange vest in it. The tug license/inventory number that was printed on the aft left side started with a XXXXX; the full number was reported via radio to ramp control at that moment.At no point did we see the drivers head move or look over to their left in any attempt to clear the direction of the turn onto the roadway before the tug proceeded outbound right in front of us. And at no point while on the roadway did the tug drivers head move to look in any direction other than forward (southbound facing) only. The tug was close enough to our aircraft we could see the drivers body clearly; and there was no reaction/recognition on their part. We believe the driver had no idea there was an aircraft was taxiing nearby. Once the tug cleared from in front of the aircraft; the FO reported the vehicle to ZZZ ramp control on XXX.XX along with their vehicle ID number that we witnessed. Afterwards we continued our taxi up to spot XX; contacted ZZZ ground and proceeded onward with the flight ZZZ-ZZZ1.