And Torres got in on the act himself after being brought off the bench on 65 minutes, instantly finding the net to add Spain's fourth on the night as they reached the Euro 2020 knockout stages in style.
It was a truly dominant display from Luis Enrique’s side from the get-go, with Slovakia limited to 34% possession and just three shots to Spain's 19 across the 90 minutes.
The 2012 winners were presented with a golden opportunity to take an early lead when Koke was judged to have been brought down by Jakub Hromada inside the area after a VAR review.
But Newcastle stopper Martin Dubravka expertly denied Alvaro Morata from twelve yards with an acrobatic save high to his right, meaning Spain have now missed 7 of their 12 European Championship penalties.
It didn’t take long for the deadlock to be broken though, and it came under fortuitous circumstances on the half hour.
Pablo Sarabia’s vicious 25-yard effort smacked against the crossbar and looped high into the air but Dubravka, attempting to tip the ball out for a corner, inadvertently bundled it into his own net.
The goal was just rewards for the hosts who, until that point, had seen several gilt-edged chances go begging as they pursued the victory needed to secure qualification.
And the three points were all but secured when Slovakia failed to properly clear a corner, allowing Gerard Moreno to clip an inviting cross past the stricken Dubravka and into the path of Laporte.
The City man rose highest to open his international account, sending an inch-perfect header back across goal and into the far corner of the net.
The scoring continued before the hour when Sarabia arrived unmarked in the area and completed a free-flowing move from Jordi Alba’s cutback.
Torres then got in on the act to add a fourth in the 67th minute, making an instant impact off the bench by sending a delightful flicked finish into the net at the near post from Sarabia’s low cross.
And in an almost mirror image of the City winger, fellow substitute Pau Torres, on for City defender Eric Garcia on 71 minutes, thought he’d found the back of the net within minutes of entering the fray when he converted Laporte’s flick.
However, the defender’s effort took a heavy deflection en route to the net, and went down as a Joraj Kucka own goal.
Despite the emphatic victory, Sweden's 3-2 triumph over fourth-placed Poland in Saint Petersburg means they top Group E with seven points, with Spain finishing one place and two points behind.
Slovakia have to settle for a third-placed finish after one win and two defeats from their three group matches, while Poland finish bottom with two points.