The match changed dynamics in the 64th minute when referee Raphael Claus conducted a video review of a collision between Balogun and Tarik Muharemović, resulting in a red card for the American striker.
Bosnia and Herzegovina increased their pressure with the numerical advantage, forcing the US defense to adjust after veteran forward Edin Džeko had already departed due to a 50th-minute injury.
The co-hosts sealed the victory when Dest earned a free-kick on the edge of the penalty area, allowing Tillman to fire a dipping effort over the wall and under the crossbar.
>>> US Men's Soccer Defeats Bosnia and Herzegovina to Reach Round of 16
The upcoming round of 16 opponent, Belgium, represents the fourth team out of five in this tournament that the US has faced in a friendly within the past year, following a previous 5-2 loss.