Ricardo Quaresma scored the winning spot-kick after Jakub Blaszczykowski's effort was saved by Rui Patricio.
Robert Lewandowski had fired Poland ahead in the second minute with teenager Renato Sanches equalising via a deflected strike.
Portugal's semi-final opponents will be either Wales or Belgium.
Remarkably,
Portugal have reached the last four without winning a game in normal
time following three draws in a group in which they finished third and
an extra-time win over Croatia in the last 16.
No side has ever got this far in a European Championship without winning a match inside 90 minutes.
Portugal
have also only led a match for 22 minutes during the whole tournament,
while Poland have not trailed for a single minute.
However, for a second dour and conservative knockout game running, Fernando Santos' side did what was required when it mattered.
How the penalty shootout was won
Neither goalkeeper came close to saving the first three penalties from either side.
Cristiano
Ronaldo, Sanches and Joao Moutinho all scored excellent penalties for
Portugal, with Lewandowski, Arkadiusz Milik and Kamil Glik following
suit for Poland.
However, after Nani had put Portugal 4-3 ahead,
Patricio dived full length to his left to palm away Blaszczykowski's
effort with one hand.
Lukasz Fabianski got his fingertips to Quaresma's decisive effort but could not prevent it finding the roof of the net.
Ronaldo's redemption of sorts
For much of the game, the overriding image of Ronaldo was of him
slapping his thigh and screaming towards the French sky in frustration.
Barring
a few exceptional moments - his two goals against Hungary and assisting
Quaresma's winner to see off Croatia - this has been a disappointing
tournament for the finest European player of his generation.
He
was barely recognisable from the figure who has terrorised defences
across the continent for more than a decade as a series of scuffed and
miscued strikes took him from 31 to 36 efforts for the tournament
without an addition to his two group-stage goals.
Worst of all was
a couple of air shots - one from a low Nani cross, the other following a
chipped ball over the defence and into the box by substitute Joao
Moutinho.
He should have had a first-half penalty, when he was
clumsily shoved in the back in the box by Michal Pazdan, but his
anguished appeals were waved away by referee Felix Brych.
However,
he led from the front in the shootout, firing home the first penalty
with aplomb and remains in the tournament, unlike Poland's own star man.
Lewandowski offers hope
Having scored 13 goals in qualifying and 42 in 51 appearances for
club Bayern Munich in 2015-16, Lewandowski had spent much of Poland's
four games prior to Thursday being frustrated, through both fair and
foul means from opponents - he is the most fouled man in the tournament.
It
was only a matter of time, though, before a striker of his class made
an impression on the tournament, although few would have imagined
Portugal to be so accommodating so early in Marseille.
Southampton
full-back Cedric Soares was at fault, allowing a cross-field ball to
evade him and reach Kamil Grosicki, whose low cross was struck home
first-time by his captain with just one minute and 40 seconds on the
clock.
It is the second fastest goal in Euros history - beaten only by
Dmitri Kirichenko's 65-second strike for Russia against Greece in 2004 - and ends a 645-minute goal-drought for Lewandowski in the finals of this competition.
Now
brimming with confidence, the 27-year-old then beat Pepe to the ball in
the box but saw his low shot saved by Patricio as Poland took the game
to their opponents in the first 25 minutes.
Unfortunately, they
were unable to build on this, offering precious little in attack and
relying instead on a resolute defence that has conceded just twice in
five games (two of which have gone to extra-time) to see give them
through to the shoot-out.
