Steven Bergwijn and Memphis Depay scored in the last six minutes to secure top spot in group G.
The Dutch return to the finals after missing out on the 2018 tournament in Russia but with little conviction after limping through their last two qualifiers.
Turkey finished second in the group after a 2-1 away win at Montenegro to secure a play-off spot.
Karim Benzema and Kylian Mbappe were on target again in a sharp second-half performance as already qualified France scored a 2-0 away win against Finland.
Finland, who were hoping to secure a playoff spot, ended up third behind Ukraine who beat Bosnia 2-0 away
Wales held Belgium to a 1-1 draw to guarantee themselves runners-up spot behind the world number ones in Group E in Cardiff.
Wales are trying to qualify for the World Cup finals for the first time since 1958.
Teams to have qualified so far from Europe are Germany, Denmark, France, Belgium, Croatia, Spain, Serbia, England, Switzerland and the Netherlands.
Another 12 teams now go into a series of play-offs for a further three spots in Qatar.