The Bosnians had lost on penalties to Northern Ireland on Thursday in the playoff semi-final but will be lifted by a dogged performance against the disappointing Dutch, particularly after starting without several key players.
The result left the Dutch, who were runners-up in the inaugural Nations League, with four points from three games while Bosnia have two.
The Dutch threatened early with defender Stefan de Vrij finding space in between the Bosnian defence in their penalty area but got only a glancing touch to a good heading opportunity in the fifth minute.
Quincy Promes booted a shot well over the top in another half chance for the Dutch and De Vrij had another glancing header in a limp first half from both sides.
Bosnia came alive when 34-year-old skipper Edin Dzeko was sent on as a substitute for the last half hour.
He was immediately involved in several breakaways, the best of which saw him set up Miralem Pjanic up for a shot that forced Dutch goalkeeper Jasper Cillessen into his first save of the game, after 68 minutes.
That stirred De Boer into making changes and two new players the right hand side quickly lifted the Dutch out of their lethargy.
Frenkie de Jong got the visitors' first shot on target in the 77th minute, turned away by Bosnia goalkeeper Ibrahim Sehic, and from the resultant corner Luuk de Jong watched in disbelief as his powerful header was also pushed around the post in a breathtaking save.
With five minutes left, Frenkie de Jong should have finished off a pull back from Steven Berghuis but defender Darko Todorovic dived to block the goal-bound effort.
In stoppage time, Ryan Babel should have snatch a late winner but blasted wide from point-blank range to sum up a disappointing night for the Dutch.