The Dutch made 137-6 to beat Namibia by four wickets with four balls remaining in their play-off in Malahide, Dublin.
Hong Kong edged out Afghanistan by five wickets, having needed 16 from the last over at the same venue.
Both the losing sides have one more chance to qualify - if they win their final qualifying play-offs on Thursday.
Malahide will again be the venue as Afghanistan face Papua New Guinea before Namibia take on Oman, with both winners booking their place in India.
All four sides in Saturday's semi-finals have already qualified for 2016, but the Qualifier continues with ICC ranking points still up for grabs.
Scotland face Hong Kong in the semis, with Ireland meeting the Netherlands, with the winners of those two games meeting in the Qualifier's final.
The Netherlands played in the World Twenty20 in 2009 and 2014 - beating England both times - while Hong Kong also qualified for the 2014 event.