While neither side set the Amsterdam Arena alight, few would argue France was undeserving of the three points as the Netherlands, a flurry of late chances aside, rarely looked like threatening.
"This is an important victory, it is deserved," Deschamps told French television. "We could have scored more goals. In the second half we had less possession, less control but coming to win here is good knowing we did not have the desired result in the first game (0-0 vs. Belarus).
"Winning here is solid and having more opportunities than them is very satisfying."
The tone of the night was set inside 10 minutes, with Kevin Gameiro drawing an acrobatic save from goalkeeper Maarten Stekelenburg.
Jeffrey Bruma's loose ball gifted possession to Antoine Griezmann, who played in his Atletico Madrid teammate but his shot was parried behind for a corner.
The Netherlands had started its World Cup qualifying campaign in good form, recording a 1-1 draw away to Sweden and dismantling Belarus 4-1 at home.
However, the Dutch were dealt a blow as Quincy Promes -- who scored twice against Belarus -- was forced off after just 15 minutes and replaced by Memphis Depay.
And it wasn't long before France's dominance paid off.
Paul Pogba, Manchester United's often-maligned record signing, picked the ball up 30 yards out and fired a rocket towards goal under halfhearted pressure from Kevin Strootman.
While the ball dipped and swerved plenty, Stekelenburg will be disappointed not to have kept it out after getting two hands to the shot.
The Netherlands haven't recorded a competitive win over France for eight years and you got a sense Danny Blind's side felt like the underdog.
The biggest roar of the match came after the Dutch claimed Laurent Koscielny blocked Vincent Janssen's shot with his hands, but referee Damir Skomina waved away their appeals.
Pogba came to the fore in the second half, playing in a more advanced position and lofted a pinpoint through ball right onto Gameiro's toe, but Stekelenburg was once again on hand to smother his attempt.
The Netherlands' only real attacking threat came from Rick Karsdorp in the right back position, as his blistering pace tormented Layvin Kurzawa all evening.
One of many marauding runs culminated in an inch-perfect pull back to Depay, but the out-of-favor Manchester United forward couldn't keep his shot on target.
It speaks volumes that Stekelenburg was the best Dutch player on the pitch by a considerable distance and his teammates had him to thank for continuously keeping the French at bay.
Once again he denied Gameiro, before saving a pointblank Pogba header.
Sensing the frustration in the stands, the Dutch finally began to press as injury time approached.
The best chance came after Anthony Martial lost possession down the right. Substitute Bas Dost headed the ball into Depay's path, but his reaction shot was palmed into the air by Hugo Lloris and eventually held.
''I think we deserved at least a point from this game," Blind said of his team's performance. "Maarten [Stekelenburg] should have saved that ball. He knows that.''
The goalkeeper agreed, referring to Pogba's goal as an "error" on his part.
Victory puts France top of Group A, level on seven points with Sweden after its 3-0 win over Bulgaria. The Netherlands sit in third, three points further back.
Meanwhile, Belgium's Christian Benteke scored the fastest goal in World Cup qualifying history, netting after just seven seconds against Gibraltar and beating the previous record of eight seconds set by San Marino's Davide Gualtieri versus England in 1993.
The Red Devils strolled to a 6-0 win, with Chelsea's Eden Hazard also getting on the score sheet.
Cristiano Ronaldo was made to play second fiddle to Andre Silva, who scored a first-half hat-trick in Portugal's 6-0 win over the Faroe Islands.
Having relied heavily on the Real Madrid star in recent years, Portugal may have finally found a striker that scores goals to ease the burden.