B737-800 Captain reported loss of #2 Hydraulic System during cruise flight. The crew performed a diversion and precautionary landing.

Narrative

Diversion to ZZZ due to Loss of System B hydraulics. We were about 5 minutes past level off at FL350; First Officer was flying; VMC flight conditions; smooth ride. First indication of a problem was Autopilot B disengaging. The First Officer took over flying manually. About 30 seconds later; we got a Master Caution Light with a HYD annunciator. We both looked at the overhead panel; at that point; the Flight Control B Low Pressure Light was the only light illuminated; followed 15-30 seconds later by both the System B ELEC and ENG Hydraulic Pump Low Pressure Lights. I started to run the LOSS OF SYSTEM B checklist in the QRH; and requested priority handling with ATC ZZZ1; and asked them to standby for our intentions. We were about 80 miles northwest of ZZZ at that point; the First Officer checked the ZZZ weather; which was VFR with winds ~200/15 (aligned with Runway XX). I informed Center that we were going to divert to ZZZ. I completed the QRH in the descent; followed by the Non-Routine Landing Considerations checklist. I notified Dispatch via ACARS 7700 page; and requested ARFF (airport rescue and fire fighting) response. Alternate Flap Extension; approach and landing were uneventful. I took the aircraft for approach and landing since First Officer had less than 50 hours in the 737. We rolled out ~7;000 feet down the runway (between XX and XY taxiways). ARFF did a visual inspection and checked the brake temperatures via their equipment--at that point we were cleared to continue taxiing to the gate. The First Officer did a post flight inspection; and did not find any significant fluid leaks (the B system was about 72% full post landing).Not a causal factor; but the low-time First Officer performed extremely well during the event--both flying the aircraft and with PM duties after I took the aircraft for landing. Not a prevention; but we did a visual approach backed up by the RNAV GPS Y Rwy XX; which has a significant offset from runway heading; and I ended up flying the approach visually; with limited input from the flight director. We would have been better loading the non-precision or RNAV approaches; which are aligned with the runway.