After a frustrating opening half for the Dutch side, it finally broke through in the 53rd minute with Sneijder's stinging drive deflected by Japan goalkeeper Eiji Kawashima into his own net.
Japan had the best chance to level the score a minute from time but an unmarked substitute Shinji Okazaki fired over the bar from just 10 yards as Netherlands held on for victory.
The result handed the Oranje maximum points from its opening two fixtures in Group E.
The Oranje, who had a sea of supporters at Durban's Moses Mabhida Stadium, dominated possession but had just one shot on goal in the opening half.
Rafael van der Vaart's 25-yard shot towards the near post proved an easy save for Kawashima.
Netherlands coach Bert van Marwijk fielded the same line-up that beat Denmark 2-0 in its group opener, with Van der Vaart, Sneijder and Dirk Kuyt playing in support of forward Robin Van Persie.
Netherlands dominated the early exchanges and created the first chance after four minutes when Van Persie's teasing cross from the left flashed across the goal and just eluded Liverpool striker Kuyt.
Shortly after, Sneijder's curled free-kick went over the bar.
At the other end, Yuto Nagatomo's right-footed strike from the edge of the area went wide.
On the half-hour mark, Yuji Nakazawa did well to clear Giovanni van Bronckhorst's cross from the right with Van Persie waiting inside the area.
Soon after, Keisuke Honda nodded high from Daisuke Matsui's free-kick. Tulio Nataka then latched onto Yasushito Endo's free-kick and his header went wide as Japan got closer.
Japan first tested Maarten Stekelenburg in the 37th minute, with Matsui's volley forcing a save from the goalkeeper.
Five minutes before the break, Honda wasted a good chance when he fired a 40-yard strike way over the bar.
Netherlands pressed forward more aggressively after the break and Van Persie twice had the chance to break the deadlock.
His weak header from Van Bronckhorst's cross proved an easy save for Kawashima and seconds later, the Arsenal striker fired wide from 15 yards.
Netherlands took the lead soon after. A poor headed clearance from Japan's defence fell to Van Persie who spotted Sneijder and the Inter Milan winger's powerful strike came off Kawashima and into the back of the net.
Japan reacted and Yoshito Okubo forced a good save from Stekelenburg with a stinging drive from 25 yards. Shortly after, Okubo fired over the bar as the Blue Samurai surged for the equaliser.
With 15 minutes remaining, the ever-present Okubo shot wide of the far post as another opportunity went by for Japan.
Substitute Ibrahim Afellay twice had the chance to put the game beyond Japan's reach in the latter stages of the match but his close-range efforts were denied by Kawashima.
With seconds left to play, Okazaki struck wide from close-range, much to the relief of the Dutch fans.