The World Cup Group B clash appeared destined to remain deadlocked as Bosnia frustrated Switzerland's possession-heavy approach before substitute Manzambi broke through in the 74th minute, three minutes after entering the game.
Vargas, also introduced late, added a second before setting up Manzambi's second, with Granit Xhaka's stoppage-time penalty completing the rout after Bosnia had been reduced to 10 men.
"It was very important that we had all of our energy on the pitch. This was our strategy," Yakin told reporters.
"We needed to be very patient and stay in the game. It was important that after the second hydration break, we changed some things. That was the edge we had. We brought on very quick players. Our opponents ran a lot and this created gaps."

Crucial timing
Yakin said the timing of the substitutions was as important as the changes themselves.
"We could have made the substitutions earlier, but then the opponent would have had the chance to react," he said. "That's why I waited for the hydration break. This was the right decision today."
The Swiss coach revealed he had already told Vargas, one of Switzerland's most dangerous attacking players, that he would have to wait for his opportunity.
"I told Vargas I would bring him on as soon as the opponents started to get more tired," Yakin said. "We brought him on at the right time. Today it was a tactical decision."
Manzambi, 20, justified the move with two goals and another lively display.
"He is a very happy person with so many football qualities," Yakin said of the Freiburg player. "He can dribble, score and put a lot of pressure on opponents. He can surprise us as much as the opponent."
Yakin also credited the hydration breaks themselves, saying they had become a tactical tool.
"During three minutes we could talk about substitutions and things we needed to change," he said. "We can use elements such as cooling breaks in our favour."
The victory moved Switzerland on to four points and put them in a strong position heading into their final group match against Canada.
Read the match report with Flashscore.
FIFA World Cup 2026
The 2026 World Cup is taking place from June 11th to July 19th in the United States, Canada and Mexico. The tournament features 48 national teams and is played at 16 modern stadiums.
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