The home side recorded a comfortable victory as they were never really troubled at the back and dominated proceedings for the full 90 minutes
Rafael van der Vaart gifted the home side an early lead when he found the net from outside the area, before Klaas-Jan Huntelaar made it two shortly after. Ruben Schaken then added his name to the score sheet after the break with a tap-in from close range to effectively kill off the game.
Oranje started the match with attacking intentions and needed only seven minutes to break the deadlock. Huntelaar set up Van der Vaart on the edge of the area, and the Hamburg star beat the Andorra goalkeeper with a shot in the bottom corner.
Andorra looked shaken after the opener and again conceded some 10 minutes later. Jeremain Lens got all the time and space he needed to send in a superb cross for Huntelaar, who somewhat fortunately deflected the ball past the glovesman with his back.
Kevin Strootman and Lens got chances to further extend Holland's lead, but the former aimed wide, while the latter blasted his shot over the bar. Bruno Martins Indi did find the net after a free kick, but his header was rightly disallowed for offside.
The hosts did get their third goal shortly after the interval, though. Lens once again went past his direct opponent down the left, before sending in a low cross toward the far post. Schaken reacted alert and beat his marker to be the ball to cap his debut with a goal.
Ron Vlaar then came close to adding his name to the score sheet, but his powerful header came back off the upright. Huntelaar, too, got a good chance to make it four, but he miraculously missed from five yards out.
Oranje sit joint first in their group with nine points from three games, and meet Romania on Tuesday in their next encounter.
Andorra have lost all three games so far and are the number last in Group D. They take on Estonia on October 16.