An own goal from visiting defender Kornel Salata on seven minutes and a fine finish from Sneijder's replacement Rafael van der Vaart on 75 minutes sealed the win for Bert van Marwijk's team, but the main talking point of the match centred around the condition of the hobbling Internazionale midfielder Sneijder just nine days before they face Denmark in their opening match of the finals.
Sneidjer seemed to be fouled by Salata early in the second half before going to ground seconds later with an ankle injury. After receiving some treatment, he returned to the action but began clutching his leg again before signalling to the bench that all was not well.
He departed the action with Van der Vaart wheeled on at Feyenoord's De Kuip stadium before Sneijder headed to the dressing room. However, Van Marwijk later played down concerns, saying the midfielder "will be fine".
With the Netherlands among the favourites to lift the Euro 2012 trophy in Poland and Ukraine, the last thing they need is an injury to Sneijder who played such a leading role in their run to the World Cup final in South Africa two years ago.
The Dutch play their final friendly on home soil before the finals against Northern Ireland in Amsterdam on Saturday with Sneijder likely to be wrapped in cotton wool for that one.
The Netherlands face their opening Euro 2012 Group B match against Denmark on June 9 in Kharkiv before meeting Germany (June 13) and Portugal (June 17) at the same venue.
Having lost to Bulgaria 2-1 in Amsterdam on Saturday, the home side seemed intent on pleasing a vociferous band of home supporters by turning on the style.
They struck the opening goal when Salata inadvertently turned Ibrahim Afellay's cross into his own net early on. Afellay tried to bend a shot beyond Jan Mucha in the visiting goal five minutes later, but the Slovakia keeper dived gratefully to prevent the ball from finding the net.
Gregory van der Wiel saw an effort deflect over the bar moments before the break, but Slovakia - who hit the bar in the opening minutes courtesy of a Marek Hamsik header - were proving to be stodgy opponents.
They should have equalised in stoppage time in the first period, but Marek Bakos slid a shot wide of goal under pressure from Everton defender Johnny Heitinga.
The Netherlands sealed the win when Van der Vaart swept a shot beyond Mucha five or so minutes after he had rattled the bar with a free-kick from the edge of the visiting area.