B737 Captain reported the loss of the B hydraulic system during cruise. The flight crew requested priority handling and make a precautionary landing at destination airport.

Narrative

Maintenance Release was clean; I did the walk around. The only noteworthy thing was the engine 2 oil access door was not secure. I looked inside and everything seemed in place and secure; I even looked inside engine 1 oil access door to make sure both sides were identical. Engine oil levels were both 97% during preflight and the hydraulic levels; though I do not remember exactly the quantities; were normal. During climbout passing FL180 the ENG 2 (hydraulic) low pressure light came on. The First Officer (FO) ran this quick and simple QRH checklist (FM 2.130.1) which just calls for the switch to be turned off. At cruise altitude we made the appropriate electronic logbook write up and noted that all hydraulic indications were mostly normal: SYS A 74% and SYS B was at 106% both systems indicated 3;000 PSI. The FO and I both looked ahead to the Loss of System B QRH procedure (FM 2.130.5) just so we were aware of what could potentially happen if we lost the whole system.Cruise and descent were uneventful until reaching approximately 12;000 ft. on the STAR when the ELEC 1 Low Pressure light illuminated. I immediately transferred the controls to the FO and got into the QRH to prepare for the alternate flap extension etc. Dispatch and ATC were notified and then I gave the purser a briefing and made an appropriate passenger address. Out of an abundance of caution we requested Runway XXR in ZZZ since it is the longest. After configuring the aircraft early and completion of the non-normal landing checklist I assumed control of the aircraft for approach and landing which were uneventful.We then cleared the runway and stopped on the taxiway for fire and rescue to make an assessment. They noted the presence of leaking fluid from engine 2. We started the APU and secured engine 2 and were followed to the gate by a fire truck. Taxi and parking were uneventful.After the parking checklist was completed we submitted another electronic logbook report for the loss of system B and conducted a crew debrief. We were greeted by Maintenance personnel for a debrief and also inflight support. I remained with the aircraft for the entire deplaning process to make sure there were no issues with any passengers (there were not; they seemed appreciative and we were still early!) and to answer any other questions from Maintenance.Before my next flight I was contacted by the Chief Pilot and debriefed with an Assistant Chief Pilot and a Flight Manager. I truly appreciate the support offered from everyone.