Although Daniel Pudil had cancelled out Frederic Kanoute’s opener for the hosts, the Spaniards regained their advantage through Luis Fabiano.
Second-half goals from Julien Escude and substitute Arouna Kone then made things comfortable before David Kalivoda grabbed a late consolation for the Czech side.
Sevilla went into the clash looking for their first points in the group after a 3-0 defeat to Arsenal two weeks ago, while Slavia, who are making their debut in the group stages of the competition, were 2-1 winners over Steaua Bucharest.
Yet despite their recent La Liga poor form, it was the Spanish hosts who made the early breakthrough after a defensive lapse from Slavia gifted Kanoute the opener after nine minutes.
The former Tottenham striker was able to pounce on a loose ball before sending a lob over goalkeeper Martin Vaniak into the bottom left corner.
Slavia quickly began to make their presence felt, however, and after home goalkeeper Andres Palop had done well to hold onto a cross-shot from Pudil, the young midfielder found the net in the 20th minute.
Matej Krajcik provided the cross for Pudil, who placed a stunning 20-yard drive into the top right corner to level matters.
Pudil tried to double his tally moments later from a free-kick but Palop rose to the challenge this time, before launching an immediate counter-attack which resulted in Luis Fabiano heading Kanoute’s cross over the bar.
But the two players combined again in the 27th minute to restore Sevilla’s advantage. Kanoute provided a neat through-ball for the Brazilian, who swept the ball past Vaniak from 12 yards.
On 58 minutes an outswinging corner from Adriano was headed on by Fabiano to Escude, who nodded the ball home from close range to give his side a two-goal cushion.
Despite their dominance, Sevilla coach Juande Ramos decided to switch things around with Luis Fabiano making way for Kone in the 64th minute.
And the decision paid dividends six minutes later as Kanoute’s clever pass split the Slavia defence, allowing Kone to race onto the ball and slot it past the hapless Vaniak.
The Czechs managed to get on the scoresheet again in the dying seconds when Kalivoda steered the ball home on the rebound, but the points already belonged to Sevilla.