The City attacking midfielder struck a superb 44th minute opener as Portugal made it three wins out of three in Group J.
Bernardo’s goal came after skipper Cristiano Ronaldo collected a pass midway inside the Bosnia and Herzegovina half before turning and picking out Bruno Fernandes in space in the middle.
In turn, Fernandes played a perfectly-weighted through ball into the box for the run of Bernardo, who waited for keeper Šehić to commit himself before dinking a brilliant left-footed strike into the far corner.
Bosnia had created several excellent opportunities either side of the break and gave Portugal much to think about.
But Roberto Martinez’s side then made sure of victory 13 minutes from time when Fernandes doubled the hosts’ advantage.
Substitute Rúben Neves found Fernandes with a curling delivery from the right and the Manchester United midfielder powered an unstoppable header into the corner of the net.
CITY+ | SIGN UP TO ACCESS EXCLUSIVE CONTENT
And Fernandes then rounded off the night by finding the target again deep into injury time to set the seal on victory.
Dias and Cancelo both played the full 90 minutes with Bernardo taken off after 87 minutes at Benfica’s Estadio da Luz.
The result kept Portugal top of Group J with nine points. They are back in action on Tuesday when the Portuguese travel to Iceland, kick-off 19.45 (UK).
Meanwhile, City goalkeeper Ederson played the full 90 minutes as Brazil beat Guinea 4-1 in a friendly international played in Barcelona, Spain.
First half goals from Joelinton (27) and Rodrygo (30 minutes) had given the South Americans a two-goal cushion before Serhou Guirassy narrowed the deficit for the African side nine minutes before the break.
However, Eder Militao’s strike restored Brazil’s two-goal cushion early in the second half.
And an emphatic win for the five-time world champions was rounded off by Vinicius Junior’s penalty two minutes from time.
