The Swansea midfielder delighted the home fans in a packed Cardiff City stadium when he robbed defender Peter Pekarik of the ball and unleashed a stinging low shot past keeper Martin Dubravka in the fifth minute.
The Slovakians, who beat Hungary 2-0 at home in their opening match on Thursday, went close to snatching a draw in the second half but were denied by a pair of superb saves from Wayne Hennessey.
The Wales keeper thwarted Albert Rusnak from close range in the 54th minute and kept out a Michal Duris header with an acrobatic save in the 74th as the visitors pressed forward relentlessly in search of an equaliser.
In between those two chances, Dubravka somehow parried a stinging Harry Wilson volley while Pekarik almost made amends for his early error when he headed inches wide of the far post in the closing stages.
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Later on Sunday, Hungary host Croatia, who came from behind to beat Azerbaijan 2-1 in their opener on Thursday.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
