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Steve Clarke's men move to the top of League B Group 2 and there were more encouraging signs for the Scots who booked their place in the Euro 2020 playoff final in midweek.
A trip to Serbia next month gives Scotland the chance to qualify for a major tournament for the first time in 22 years.
But a good Nations League campaign could also provide the opportunity to reach the World Cup in 2022.
Clarke made four changes to the side that needed Scotland's first ever penalty shootout to see off Israel in midweek and was rewarded with a more commanding performance.
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Australian-born Dykes took his tally to two goals in four appearances for his adopted country by sliding home Stephen O'Donnell's fine cross on 54 minutes.
Slovakia ended the Republic of Ireland's hopes of reaching next year's European Championships in the playoff semi-finals on Thursday, but a much-changed side picked by Pavel Hapal rarely threatened.
Oli McBurnie came close to his first Scotland goal when the Sheffield United striker's header came back off the crossbar late on.
But one goal was enough to keep the hosts one point clear of the Czech Republic, who visit Hampden on Wednesday.
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