Johnson hit the post and narrowly missed two other opportunities and Eloy Colombano fired into the side netting after rounding keeper Joe Cannon, who twice saved sharply on misdirected clearances by teammate Troy Roberts.
Cursed by bad luck with injuries and other factors many times this season, this time the Galaxy parlayed a few breaks into three points. It took one shot on goal and made it count.
Referee Baldomero Toledo handed out straight red cards to Jimmy Conrad and Davy Arnaud for studs-up tackles on Galaxy midfielder Pete Vagenas (what did he ever do to them to warrant such treatment?), and it was while playing 11 against 10 with Conrad out of the match Los Angeles (6-13-6) got its goal.
Mike Randolph, who started the game at left back and moved up to midfield when Ante Jazic entered the game after Conrad's ejection, hit a cross from the left flank that nicked off Kerry Zavagnin and looped into the goalmouth for Glinton to nod home. One of Conrad's strengths is clearing crosses and balls in the air, but in his absence Glinton found a seam.
Kansas City sits seventh in the overall standings with 36 points, five more than ninth-place Columbus, but must play D.C. United Oct. 5 without Conrad and Arnaud in its final home game, then closes out the season at New York and Dallas.
If it fails to win any of those final three games, two pursuing teams could edge it out of the playoff octet, including Los Angeles (24 points), which has five more games to play.
During the run-up to David Beckham's arrival, the odds he could spark a playoff push provoked great debate. His twisted knee all but killed off that talk, except within certain sections of the Galaxy organization directly controlled by Coach Frank Yallop.
If the Galaxy can win in Columbus Sunday, its postseason chances will still be scant, but the debate will rage anew.
Sept. 27 in Kansas City
Kansas City 0 Los Angeles 1. Goal: Glinton (Randolph) 80.
Kansas City - Hartman, Jewsbury, Conrad, Garcia, Harrington, Arnaud, Marinelli, Zavagnin (John, 89), Burciaga Jr. (Watson, 85), Johnson, Colombano (Victorine, 65).
Los Angeles - Cannon, Klein, Harden, Roberts, Randolph, Martino (Jazic, 62), Tudela, Vagenas, Jones (Glinton, 71), Donovan, Gordon (Pavon, 77).
Yellow Card: Los Angeles - Harden 76.
Red Cards: Kansas City - Conrad 57, Arnaud 82.
Referee: Baldomero Toledo.