Air carrier Captain reported while in cruise noticing a burning electrical odor resulting in the flight diverting as a precaution.

Narrative

During cruise flight at FL370; at approximately XA20Z; about 100NM west of ZZZZZ; I noticed a faint burning electrical odor. I asked my FO if he smelled the same thing; but he did not. Ten minutes later; we both smelled a burning electrical odor again--this time; a much stronger puff" coming from the vents located at the base of both the left and right windshields. It was not continuous; just a strong; brief "puff.". I contacted the FM and asked him to inspect all lavatories and walk through the aircraft. He reported detecting an odor near row 27. We contacted Dispatch and proposed diverting to ZZZ; as we were only 200NM away. Dispatch agreed. We contacted ATC and requested the diversion as a precaution. We ran the necessary checklists; diverted; and landed uneventfully in ZZZ. We swapped aircraft and continued to ZZZ1. No emergency was declared. I filled up 'smoke' questioner; and let Maintenance Control troubleshoot. Since the odor was not continues; and sporadic; we did not run an entire smoke/fire/fumes Non-Norrmal checklist QRH. In the retrospect and after the even; I believe we should have run the checklist as a precaution. In addition to threats; I would like to add a 'Diversion' as this added a time pressure to have A/C FMC properly programmed; brief the STAR and approach procedure; get FA ready and inform pax of our precautionary diversion. Nothing unusual in this situation; however; I don't see this option in 'Threats' below."