The Manchester United duo of Diogo Dalot and Bruno Fernandes were on the scoresheet as Portugal picked up three points in Prague.
Dalot prodded home from just six-yards out 33 minutes into the game before Fernandes doubled Portugal's lead on the brink of half-time.
Czech Republic failed to capitalise on a golden opportunity deep into added time. Patrik Schick blazed a penalty over the crossbar after VAR intervention penalised Cristiano Ronaldo for a handball.
Dalot added a third before a late Diogo Jota header put Portugal 4-0 ahead with little time left in the game.
Portugal's perfect night was made even better with Switzerland's 2-1 victory in Spain, moving Portugal into pole position for a spot in the final four of the UEFA Nations League.
A point in their clash with Spain on Tuesday night would see Portugal progress.
With tonight's results, Czech Republic have fallen to the bottom of the group, two points off safety. Tuesday's trip to St Gallen has become a must win, with anything less seeing them relegated from the top tier.
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Story of the match
Jaroslav Silhavy set up his side in a 3-4-2-1 formation, with his wide players causing issues early on.
Vaclav Jemelka and Schick both fired shots over the bar within the opening five minutes, taking advantage of a slow start from the visitors.
Portugal's first real chance came nine minutes in. Bernardo Silva's cross looked to find Ronaldo in the penalty area, but it was cleared to Ruben Neves who flashed wide of goal from 20-yards out.
Ronaldo was in the thick of the action just four minutes later after a horrible collision with Czech keeper Tomas Vaclik.
William Carvalho's lofted ball saw the duo contest in the air, before the keeper connected with Ronaldo. The striker was assessed by medics, who managed to stop blood pouring from the striker's head.
Things would not get much better for Ronaldo just moments later. A slick Portugal move saw Bruno Fernandes find an unmarked Ronaldo just eight-yards out from goal, but the United striker failed to get any significant connection on the ball.
It looked as though Portugal were not going to take their chances, as Mario Rui's cross went uncontested just before the half hour mark.
Fernando Santos' men appeared to begin to get frustrated, but they made their pressure count in the 33rd minute.
Diogo Dalot drove with the ball from deep before playing it wide to Fernandes. His Manchester United teammate put in a fantastic cross that evaded everyone in the middle, before Rafael Leao put the ball back across goal for Dalot to poke home from close range.
Portugal could have doubled their lead eight minutes later, but Ronaldo blazed a volley wide of the goal after a spectacular cross-field ball from Fernandes.
It was 2-0 in the second minute of additional time as Fernandes got himself on the scoresheet.
Mario Rui played a beautifully weighted cross for an unmarked Fernandes to capitalise on just six-yards out.
It was all plain sailing for the visitors up until the fifth minute of time added on. A Czech Republic corner took a slight deflection and struck the hand of Ronaldo, with the referee waving away all appeals.
After checking the VAR monitor, the decision was overturned and the penalty was awarded.
Game over
Schick stepped up to take the penalty, but his effort clipped the top of the crossbar and went into the stand.
If the game was not already over, it was after the missed penalty. The score remained 2-0 to the visitors going into the half-time break.
Czech Republic did improve in the second half. They looked to press Portugal higher up the pitch, but did not create any clear cut chances to show for it.
Dalot compiled Czech misery in the 52nd minute, scoring a spectacular left footed effort. The full-back found himself 30-yards out from goal in midfield.
He cut back onto his left foot and placed a curled finish into the bottom corner, killing the game off for good.
After the third goal, the game slowed down with Portugal seemingly content with the 3-0 win.
A triple change by Silhavy injected life into a deflated Czech side, although again they failed to make their pressure count.
Portugal substitute Diogo Jota wrapped up the three points with a fourth goal eight minutes from full-time.
Ricardo Horta's corner was glanced on by Ronaldo, with Jota all alone at the far post to head home.
Supporters inside Sinobo Stadium made their feelings clear at full-time, as fans booed and jeered their players off the pitch.
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Player of the match
This could have been one of a number of Portugal players, but Dalot could not be overlooked on the night.
The United man scored his first two international goals from unexpected positions given that he was playing at right back.
His defensive game was just as good, stopping Czech attacks on numerous occasions.