The Ajax defender had yet to score for the national team coming into the game, but opened his account early on with a good header from a corner.
Arjen Robben doubled the lead with a penalty before Veltman got his second of the evening after another corner, with Davy Klaassen and Vincent Janssen completing the scoring after the break.
The win comes as a welcome boost for Netherlands ahead of Friday's World Cup qualifier against Luxembourg, for which Dick Advocaat will be in charge following Fred Grim's interim stint.
Netherlands currently sit fourth in Group A with seven points from five games and cannot afford to slip up again if they are to have a chance of making it to the finals in Russia.
Ivory Coast started the match with attacking intentions and came close to an early opener when Giovanni Sio tested Jasper Cillessen with a powerful shot from a narrow angle after being set up by Jean Michael Seri.
The Dutch slowly grew into the game after a difficult start and Veltman handed the hosts the lead in the 13th minute following Memphis Depay's corner from the left, placing a header past the helpless Badra Sangare after being left totally unmarked.
— OnsOranje (@OnsOranje) June 4, 2017
Netherlands were then fortunate not to concede an equaliser when Maxwel Cornet's fine header hit the upright, before Robben doubled their lead in the 32nd minute by coolly converting from the spot after Sangare had clumsily brought down Janssen inside the area.
The home side continued to cause Ivory Coast all kinds of trouble from set-pieces and Veltman doubled his personal tally 10 minutes before half-time, beating Sangare with a volley from close range after again escaping the attentions of his marker.
Janssen should have made it four early in the second half after some good work from Robben, but the Tottenham striker hesitated too long and failed to test the goalkeeper, wasting another gilt-edged chance soon afterwards when he aimed just wide after sending Sangare in the wrong direction.
Grim's men continued to dominate proceedings and Depay was unfortunate when Sangare produced a magnificent finger-tip save to push his superb long-range strike onto the crossbar.
But there was no denying Netherlands and Klaassen eventually did make it four in the 69th minute with a cool finish after being set up by Janssen.
Grim then brought on Wesley Sneijder for Klaassen to make the Galatasaray playmaker the joint most capped player in Dutch history, level with Edwin van der Sar on 130 games.
And the 32-year-old had reason to celebrate shortly after his arrival when Janssen got his goal at last, tapping home a rebound after Sangare failed to hold to Georginio Wijnaldum's shot.
130 - Wesley Sneijder has equalled Edwin van der Sar as the most capped player in the history of the Netherlands (both 130 caps). Legend. pic.twitter.com/iykrL9aVUj
— OptaJohan (@OptaJohan) June 4, 2017