Bay coach Brett Angell substituted newcomer Ben Everson at the coal face with Argentine striker Facundo Barbero in the 63rd minute after the Englishman again looked to out at sea in his second outing.
In the 79th minute substitute Angus Kilkolly had the Bay's best chance of an equaliser as he ran for a one-on-one with City goalkeeper Enaut Zubikarai Goni and a defender in pursuit but his finishing lacked impetus although he looked dazed from Spaniard Goni's clearance that had clipped him on the noggin only minutes earlier.
Angell yanked off Matsumoto, who also had a hot-and-cold game, and injected James Hoyle.
The Bay, fifth on the ladder before the kick off, eventually threw the kitchen sink at City in the dying minutes but the Ramon Tribulietx-coached seemed content to concede a flurry of yellow-card fouls to maintain their slender lead.
It's fair to assume the hosts did the minimum required, including taking off Lea'alafa, to avoid risking injuries before jetting off to Japan for the Club World Club Championship on Monday.