Slavia's 23-year-old striker Peter Olayinka was dangerous throughout and put the visitors ahead shortly after the hour mark by turning in a rebound from close range. Inter won its opening three matches in Serie A to open up a two-point lead atop the Italian league but Antonio Conte's side struggled from the start against the Czech champion, putting only one shot on goal in the first half.
Making matters more difficult, key Inter midfielder Antonio Candreva went off shortly after the break with an apparent injury. Slavia beat CFR Cluj 1-0 twice in the playoffs to qualify for the group phase, having given eventual champion Chelsea a strong challenge in last season's Europa League quarterfinals, losing on 4-3 aggregate.
Barcelona was visiting Borussia Dortmund later in the other Group F match. Slavia nearly doubled its lead but a free kick from Nicolae Stanciu went just wide and then an attempt from Lukás Masopust sailed high.
Slavia goalkeeper Ondrej Kolár, who was also a key to the success against Cluj, prevented Inter from scoring a late winner when he made a one-handed save to deny Romelu Lukaku's header in the final minutes of injury time.
Slavia had lost all of its six previous matches in Italy.
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