Victory for Austin and Montreal see MLS play-off spots confirmed
Goalkeeper Brad Stuver (31) was the hero for Austin, saving twice in the shootout before Salt Lake's Tate Schmitt (27) blazed his penalty over the bar as the Texan club sealed a 3-1 shootout win after the game had finished 2-2 following extra-time.
Austin will now play either Dallas or Minnesota in the Western Conference semi-finals.
Austin had forced extra-time deep into stoppage time, when Real midfielder Scott Caldwell was ruled to have handled as he attempted a block near the edge of the area.
Striker Sebastian Driussi stepped up to roll in the spot-kick to the relief of Austin's 20,738-capacity crowd at Q2 Stadium.
The equalizer was cruel on Real Salt Lake, who looked as if they had done enough to hang on for victory after defending a 2-1 lead for most of the second half with only 10 men following Rubio Rubin's 53rd-minute dismissal for a second bookable offense.
Real had stunned the home crowd in the opening minutes of the first half, taking a 2-0 lead after a quarter of an hour.
Venezuelan international Sergio Cordova headed the visitors into the lead after three minutes, glancing a header into the bottom right hand corner from an inviting cross by right back Andrew Brody.
Cordova then doubled Salt Lake's lead with a penalty spot on 15 minutes, calmly stroking home his spot-kick into the bottom corner after Colombian defender Jhojan Valencia handballed.
Austin rallied and Driussi reduced the deficit in the 31st minute when he was given time and space to head home from Diego Fagundez's cross from the left.
Austin looked poised to equalize after a bright start to the second half but were left ruing two glaring missed chances from Argentinian forward Emiliano Rigoni.
Rigoni should have leveled just after half-time but somehow scooped his shot over the bar from just three yards out.
Rubin's sending off followed shortly afterwards, before Rigoni squandered another opportunity, heading tamely wide from Jon Gallagher's cross.
Driussi had the ball in the net in extra-time but was ruled offside before the game went to penalties.
Stuver saved from Brody and Braian Ojeda in the shootout before Schmitt's miss sealed Salt Lake's fate.
In Sunday's other game, a second-half strike from Montreal's rising star Ismael Kone (20) was enough to send the Canadian squad into a last-four meeting against either New York City FC or Inter Miami, who meet on Monday.
Ivory Coast-born Kone pounced on a through ball from forward Djordje Mihailovic in the 68th minute to score the game's first goal.
The highly rated 20-year-old midfielder, expected to be selected for Canada's World Cup squad, took one touch and finished coolly past Orlando's Peruvian international goalkeeper Pedro Gallese.
Montreal sealed the win in the final minute of stoppage time with Mihailovic burying a penalty to make it 2-0.
