PSV attacker Gakpo has been one of the breakout stars of the tournament and impressed again at Al Bayt Stadium, setting the Oranje on their way to victory with a clinical 26th-minute strike.
As Senegal defeated Ecuador elsewhere, a further goal from Frenkie de Jong made sure of a straightforward victory to clinch first place in the pool.
Gakpo likely would not have had such a prominent role thus far if not for Memphis Depay's hamstring injury, but the pair started together on Tuesday and will now aim to link up again in the last 16 against the Group B runners-up.
The Netherlands immediately looked more threatening for having Depay in the line-up, although he failed to get a shot away in an early scramble in the box, leading Daley Blind to aim tamely at Meshaal Barsham, and soon lashed over.
It was Gakpo who instead delivered the goods once more following a lovely move, laying the ball off to Davy Klaassen and taking the return to fire a firm finish into the bottom-right corner.
Dreadful defending from Qatar then allowed Louis van Gaal's men to double their lead four minutes into the second half as Barsham blocked from Depay but De Jong was able to beat two men to the rebound in front of the goal line.
A third for Steven Berghuis was ruled out for a handball by Gakpo in the build-up, with the substitute also hitting the bar in stoppage time, but events in the other match meant the Netherlands' position was never under threat.