The Dutch top Group D with 15 points after five matches and host Romania on Tuesday.
In a dull first half, the hosts lacked the necessary urgency to create an opening but a minute after the break Sneijder's replacement, Rafael van der Vaart, netted following good work from Daryl Janmaat.
Janmaat picked up his second assist 19 minutes before time when Robin van Persie scored from close range to double the lead and Ruben Schaken fired home the third after 83 minutes.
"We tried a passing game in the first half although our positional play was not good and our midfielders did not pass accurately enough or did not pass at all," Netherlands coach Louis van Gaal told reporters.
"We set that straight at half-time and then you are lucky as coach when you open the scoring so early in the second half. From that moment on it became easier for us as they could not defend so tightly anymore."
With Sneijder back after missing the last four internationals, Dutch expectations were high but the Galatasaray player never delivered and wasted a chance to open the scoring after 27 minutes when he fired wide from close range.
Minutes later Sneijder limped off with a suspected groin injury but with Van der Vaart on, Netherlands flowed better in attack.
Nevertheless Estonia, who had scored only one goal in their four previous qualifying matches, came close to opening the scoring on the verge of half-time but Konstantin Vassiljev was denied twice by goalkeeper Kenneth Vermeer.
Van der Vaart operated more closely behind central striker Van Persie than Sneijder did and it made a difference for his opening goal.
Van Persie could hardly miss to make it two while Schaken's third goal, a tight angled shot, was the 1,500th for the Dutch team.
Estonia still had chances in the second period with Martin Vunk shooting over 11 minutes before time when he looked well-placed.
