Eduardo Vargas blew a one-on-one chance against Rui Patricio, and Andre Silva fired at Claudio Bravo at the back post.
In the second half, Chile went closest as Arturo Vidal thundered a header over, and Vargas's clever overhead kick was beaten away by Patricio.
Claudio Bravo (Chili) face à Ricardo Quaresma (Portugal)
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Chile should have had a penalty, but no VAR was used for Jose Fonte's challenge, and Vidal and Martin Rodriguez hit the bar in the same attack.
In a dramatic penalty shootout, Ricardo Quaresma, Joao Moutinho and Nani all had their penalties saved.
Claudio Bravo of Chile celebrates saving a penalty in a shootout during the FIFA Confederations Cup in Russia
Image credit: Getty Images
Why was Fonte's challenge not referred to VAR? Francisco Silva was plainly fouled in the box by Fonte, and yet nobody intervened to rectify the situation. The match should have ended in Chile's favour before penalties were taken.
MAN OF THE MATCH
Claudio Bravo (Chile): He has been awful for Manchester City, so much so that he is unlikely to play for them again. But against Portugal he was back to his best, saving whatever came his way in normal and extra time. He came into his own for the penalties, though, pushing to the limit his use of early movement, and standing up to Nani's stuttering run-up to win the match.
6' - VARGAS CHANCE - Vargas is slipped in down the middle, and he's one on one with Patricio. It's a great pass from Sanchez, but Vargas wastes it by playing it straight at Patricio.
7' - ANDRE SILVA CHANCE - Ronaldo finds Andre Silva with a measured cross to the back post. Silva fires in at goal, but Bravo is across well to block.
28' - ARANGUIZ HEADER - Aranguiz meets a cross from the right from Isla, at the near post but well out, and it loops just wide and high of the far post.
54' - VIDAL HEADER - The ball is curled in for Vidal, centrally placed and eight yards out. He gets in across Eliseu, and he sends Beausejour's cross frustratingly over the bar.
57' - PATRICIO SAVE - Patricio with a good save. Vargas picks up a bobbling ball from a corner, flicks it up with his back to goal and sends a low, overhead kick at goal that Patricio does well to palm away.
95' - SANCHEZ HEADER - Isla pings in a cross from the right for Sanchez, and he sends a bullet header just a few inches wide, spinning agonisingly away.
113' - SILVA PENALTY? - Silva bursts into the box. Fonte trips him (it's clear on the replay), and the referee waves play on. Shall we have a review? Isn't that the point?
118' - VIDAL HITS THE BAR - Sanchez cuts the ball back to Silva. His cross comes to Vidal who lashes a shot at the goal, but it strikes the post. It comes out to Rodriguez and he toes an effort, with Patricio grounded, on to the bar.
PENTALY SHOOT-OUT: Chile 3-0 Portugal. NANI MISSES - A dreaful penalty. A stuttering, slow run-up sees Bravo keep his nerves. Nani punts it gently to his right, and Bravo leaps across to save.