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Alvaro Morata missed an early chance to fire Spain into the lead at the Estadio La Cartuja on Tuesday after he was denied from the spot-kick.
However, Luis Enrique's men took the lead in the Group E clash after Dubravka's shocking howler.
Slovakia were placed under pressure after Lubomir Satka lost the ball in his own half following a sloppy pass.
Pablo Sarabia received the ball from 25 yards out and the Paris Saint-Germain player fired a rocket of a strike that rattled off the crossbar.
The ball proceeded to loop high into the air and Dubravka positioned himself under the crossbar as he waited for it to come down.
However, Dubravka made a complete mess of the clearance after he flapped the ball into the Slovakia net as it dropped under the crossbar.
The 32-year-old Newcastle goalkeeper had his hands in his face and appeared frustrated with his error.
One Twitter user posted: "As a fellow goalkeeper, I've been there. Not a good feeling. The loneliest position on the pitch. Head up, Dubravka. You're still quality."
Someone else wrote: "The greatest part of this is the understated fist bump of support from his teammate at a real low point."
While a third said: "Oh dear. Martin Dubravka did not cover himself in glory with that one."
And a fourth added: "For Dubravka to do that on the world stage is just horrendous. What goes through goalkeepers' heads sometimes?"
Spain doubled their lead going into half-time after Gerard Moreno found Manchester City centre-back Aymeric Laporte, who fired home a header into the corner of the Slovakia net.
Full-time result: Spain built on their first-half advantage by thrashing Slovakia 5-0 at the Estadio La Cartuja. Goals from Pablo Sarabia, Ferran Torres and Juraj Kucka in the second half sealed all three points for Luis Enrique's men.
La Roja finished second in Group E, two points behind first-placed Sweden. Slovakia finished third while Poland came fourth.
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