LAFC claim narrow win over Whitecaps to secure progression in MLS playoffs
Bogusz's 62nd-minute strike settled a tense battle at LAFC's BMO Stadium, giving Los Angeles a 2-1 victory in the best-of-three first-round series.
Los Angeles, the top seeds in the Western Conference, had been thumped 3-0 by the eighth-seeded Whitecaps in game two of the series on Sunday.
However, Steve Cherundolo's side produced an improved defensive effort to frustrate Vancouver for long periods in Friday's decider.
The breakthrough finally came midway through the second half as Los Angeles punished a sloppy clearance from Vancouver goalkeeper Yohei Takaoka.
Takaoka's kick upfield found Los Angeles defender Aaron Long who headed forward towards the edge of the area.
The ball was helped into the path of Bogusz, and the Polish striker's first touch took him past Ranko Veselinovic before he rifled a low shot into the bottom corner.
Vancouver upped the tempo after the goal but struggled to carve out much in the way of chances as they chased an equaliser that could have sent the game to a penalty shoot-out.
Centre-half Tristan Blackmon had the ball in the Los Angeles net in the 74th minute but his header was correctly ruled offside.