The 2010 World Cup finalists did not have an easy evening, but three goals after the interval eventually helped them to victory
Louis van Gaal's men were unable to break the deadlock before the break, but Rafael van der Vaart gifted Holland the lead only minutes into the second half. Oranje continued to dominate after the opener and Robin van Persie eventually made it two, before Ruben Schaken secured the points.
The home side started the match with attacking intentions, yet struggled to create any chances of note early in the game as Estonia defended well. Wesley Sneijder tried his luck from long range twice, but his first attempt went over the crossbar while his second shot lacked power.
Oranje first looked dangerous around the half-hour mark when Daley Blind found Van Persie with a fine cross from the left. The striker then set up Sneijder, who fired wide from inside the area.
An Arjen Robben free-kick shortly after almost led to the opener, but Sergei Pareiko was alert and kept the ball out. The Bayern man again threatened minutes later when he danced past two opponents, only to aim just wide from a narrow angle.
Van Persie had by then already seen a goal disallowed for offside, while Robben saw his cheeky lob cancelled for the same reason.
Estonia were initially happy to sit back and defend, yet they came close to grabbing the lead in the closing minutes of the first half. Sander Puri cut inside from the right before setting up Konstantin Vassiljev in the centre of the pitch. The midfielder blasted a powerful shot toward the Dutch goal, which was only just parried by Kenneth Vermeer, who also kept out the rebound.
But the Dutch started the second half superbly and needed only two minutes to break the deadlock. Daryl Janmaat charged forward down the right and reached substitute Van der Vaart with a low pass inside the area. The HSV man controlled the ball with his back to goal and turned before beating Pareiko with a low shot.
Van Persie could have doubled Oranje's lead only moments later after a superb cross from Van der Vaart, but his header lacked both power and accuracy. The former Arsenal man again failed to find the net at the hour mark, when his right-footed shot from close range went over the cross-bar after some good work from Janmaat.
Nevertheless, the prolific forward got his goal at last in the 72nd minute. Once again Janmaat sent in a dangerous cross from the right, and the unmarked Van Persie volleyed home from five yards out.
Estonia should have pegged one back 10 minutes before the final whistle when Martin Vunk was clean through on goal after a superb pass from Vassiljev. However, the Sillamae Kalev midfielder failed under pressure and blasted his shot over.
Holland poured even more salt in the guests' wounds in the closing stages of the game. A Van Persie cross fell to Schaken at the far post, and the Feyenoord winger had no trouble finding the net from a narrow angle.
The result leaves Netherlands top of their group with 15 points from five games, with their next match at home against Romania on Tuesday.
Estonia sit fifth in Group D with three points from five encounters. They take on Andorra on March 26.