Brian Brobbey had put the visitors ahead midway through the first half, beating Tarik Muharemovic in the air to nod home from Noa Lang's inswinging delivery, scoring his first international goal in the process.
However, after being more of a threat following half time, Bosnia found an equaliser with roughly a quarter of the game remaining, with Ermedin Demirovic converting on the rebound after Mark Flekken had kept Edin Dzeko's initial effort out.
The visitors were dominant throughout the first half, and on debut, Bosnia keeper Martin Zlomislic kept out Dutch skipper Stefan de Vrij's powerful effort early on.
Joshua Zirkzee also should have doubled the lead late in the first period but squandered an opportunity with the goal gaping, and they were handed warning signs when Dzeko was denied shortly after the interval and then had a goal disallowed for offside.
Following the equaliser though, the Dutch barely threatened the Bosnian goal despite the introduction of Cody Gakpo, Donyell Malen and Wout Weghorst from the bench, and Jorrel Hato's late effort sailed a long way over the bar with the game ending level.
After restoring some pride following a 7-0 loss in Germany at the weekend, this result still means that Bosnia remain winless in all of their 12 League A matches in the Nations League, and are winless in their last 12 matches in all competitions.
The shape of Group A3 was already known before this evening's matches, as Bosnia's relegation to League B had been confirmed, and the Dutch knew they would be finishing second behind Germany.
That means Ronald Koeman's side will be drawn against one of France, Portugal or Spain, and will play the second leg away, in the Nations League quarter-finals in March.
BOSNIA-HERZEGOVINA VS. NETHERLANDS HIGHLIGHTS
Brobbey goal vs. Bosnia (24th min, Bosnia-Herzegovina 0-1 Netherlands)
The mounting Dutch pressure has finally told, as Lang's excellent left-wing delivery is met by Brobbey, who outjumps Muharemovic to beat Zlomislic in the Bosnian goal from inside the six-yard box.
Demirovic goal vs. Netherlands (67th min, Bosnia-Herzegovina 1-1 Netherlands)
Finally something for the Bosnians to cheer! Some excellent quick passing on the left flank between Samed Bazdar, Dzenis Burnic and Demirovic eventually sets up Dzeko, and after Flekken keeps out his well-struck effort, the Stuttgart man is on hand to nod home from close range on the rebound.
MAN OF THE MATCH - ERMEDIN DEMIROVIC
The Dutch looked impressive in the first half, but sluggish in the second, and as one part of a three-pronged attacked, Demirovic spearheaded the Bosnia fightback, being first to react on the rebound to score the equaliser which ultimately decided the outcome of the match.
BOSNIA-HERZEGOVINA VS. NETHERLANDS MATCH STATS
Possession: Bosnia-Herzegovina 36% - 64% Netherlands
Shots: Bosnia-Herzegovina 8 - 12 Netherlands
Shots on target: Bosnia-Herzegovina 3 - 2 Netherlands
Corners: Bosnia-Herzegovina 3 - 5 Netherlands
Fouls: Bosnia-Herzegovina 17 - 11 Netherlands
BEST STATS
WHAT NEXT?
Netherlands will discover their next opponents - either France, Spain or Portugal - in the quarter-finals of the Nations League when the draw is made on Friday in Nyon.
Bosnia's relegation means they will go straight into 2026 World Cup qualifying in the spring, and that draw will be made in Zurich in December.