Propper’s goals came either side of an Arjen Robben effort and Dick Advocaat’s side move back above the Bulgarians into third place in European qualifying Group A.
They are three points behind France, who host Luxembourg later, and Sweden, 4-0 winners away in Belarus.
But with Sweden to visit Amsterdam in the last round of matches next month, the three-time World Cup runners-up still stand a chance of making it to Russia after missing out on Euro 2016.
Nevertheless, the best they can hope for is surely second place and a play-off, with the French on course to top the group after destroying the Dutch 4-0 in Paris last Thursday.
Advocaat made three changes from that game, with Wesley Sneijder one of those to drop out as Lyon full-back Kenny Tete, Feyenoord’s Tonny Vilhena and Propper came in.
Propper, who left PSV Eindhoven for English Premier League newcomers Brighton and Hove Albion in the summer, was the benefactor of good play from Daley Blind as he made it 1-0 inside seven minutes.
Georgi Kostadinov headed against the post soon after for the Bulgarians but the Dutch eventually doubled their lead midway through the second half as Blind again provided the assist for captain Robben to net from inside the six-yard box.
Kostadinov stooped to pull one back for Bulgaria before Quincy Promes set up Propper to head in and make it 3-1 with 11 minutes remaining.
Sweden got their own qualification bid back on track after a 3-2 defeat in Sofia on Thursday as they outclassed Belarus, racing into a three-goal lead by the interval.
The RB Leipzig winger Emil Forsberg took advantage of poor defending to roll in the opener and Christoffer Nyman then dispossessed Mikhail Sivakou before making it 2-0.
More awful defending saw Forsberg square for Marcus Berg to make it 3-0 eight minutes before half-time and it was a foul on Forsberg that led to Sweden being awarded a penalty late on that Andreas Granqvist converted to complete the victory.
Croatia’s Mario Mandzukic (L) and Domagoj Vida go for a header during a FIFA World Cup 2018 qualification match against Kosovo in Zagreb on September 3, 2017
Earlier on Sunday, centre-back Domagoj Vida’s goal gave Croatia a crucial 1-0 victory over Kosovo in a match that had been stopped on Saturday due to heavy rain and a waterlogged pitch in Zagreb.
The Group I encounter resumed in the 21st minute on Sunday with Vida scoring 16 minutes from the end. The win took Croatia back above Ukraine to the top of the table.
Belgium can clinch qualification later on Sunday by beating Greece in Piraeus — that would give them an unassailable advantage at the top of Group H.
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