The Slovaks now need other results to go their way as only the eight best runners-up from the nine European qualifying groups advance to the playoffs.
"We still have some games to succeed so we are hopeful," Slovakia's captain Marek Hamsik said. "We deserved to win and we will all be definitely watching. It's not in our hands so we need to keep our fingers crossed."
The Slovaks spent most of the night in Malta's half and were rarely troubled as the visitors failed to register a single shot on target.
Adam Nemec grabbed his first goal in the opening half and his second in the 62nd minute, when Milan Skriniar took the ball from a defender and played it to Nemec, who took one touch and slotted a left-foot shot into the net.
Jan Kozak's side kept the pressure up and Ondrej Duda made it 3-0 seven minutes later after lunging past a defender with an outstretched leg to finish from Albert Rusnak's cross.
Slovakia last qualified for the World Cup in 2010, marking their only appearance at the tournament since splitting from the Czech Republic in 1993.
(Reporting by Michael Kahn in Prague; Editing by Christian Radnedge)
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