Trailing 2-1 in the 89th minute, Steele unleashed a left-footed shot that went through the legs of defender Andrew Baptiste for a stunning equalizer.
Then, 3 minutes into stoppage time, Beckerman snapped a shot into the left corner of the net for the game-winner as RSL (3-1-0) won for the third time in four games to start the season.
Alvaro Saborio also scored for the winners.
Darlington Nagbe netted both goals for the Timbers (1-2-1), who lost for only the second time in eight home games stretching back to last season.
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