Bosnia and Herzegovina always knew boosting their goals-scored column would enhance their chances of advancing to the knockout stage for the first time. It was no wonder, then, that thousands of their supporters went berserk when Ermin Mahmic added a potentially crucial third goal in a victory that eliminated Qatar. The goal of the game undoubtedly belonged to the exciting 18-year-old Kerim Alajbegovic, but Mahmic’s sealed a win that means a last-32 date with the USA in Santa Clara, at the home of the San Francisco 49ers, is the most likely scenario from here.

It was impossible to ignore the sense that Bosnia and Herzegovina’s head coach, Sergej Barbarez, was keeping his powder dry by keeping Alajbegovic on a leash of sorts after declining to start the teenager in their opener against Canada. After all, Alajbegovic was instrumental in Bosnia and Herzegovina arriving to this point, entering as a gamechanging substitute in playoff wins over Wales and then Italy, scoring penalties in both shootout victories, including the decisive spot-kick in Cardiff.

Edin Dzeko, this his 150th cap, is the nation’s undoubted icon but in Alajbegovic they possess one of the most exciting talents in Europe. “If you see a boy like that in the two most important games of his career so far, it means that this boy has something and quality,” Dzeko said on the eve of the tournament.

Bayer Leverkusen were so impressed with his performances for RB Salzburg last season that in March they activated the €8m buyback clause to re-sign him on a five-year contract. Alajbegovic has proven a reliable fire-starter from the bench but thrived on his second successive start and the seventh of his international career. His goal approaching the half hour was a beauty, an off-balance Alajbegovic spanking a shot into the top corner past the Qatar goalkeeper Mahmud Abunada. Alajbegovic picked up Ivan Basic’s pass outside the box and moseyed from left to right, jinking past a couple of white shirts before blasting in from 20 yards.

By that point Abunada had been kept busy, saving from Ermedin Demirovic inside 70 seconds and then Ivan Sunjic a minute later. It was Sunjic, who spent five years at Birmingham City and now plays for Pafos, who extinguished Qatar’s first attack, making amends for losing the ball on the edge of the opposition 18-yard box by racing 70 yards to toe-poke the ball away from Akram Afif. Basic then registered another effort, his dipping strike landing on the roof of the Qatar net.

Qatar struggled to repel Bosnia and Herzegovina and Barbarez’s side doubled their lead five minutes after opening the scoring. The 40-year-old Dzeko wheeled away in celebration but his attempt to cushion a diagonal pass into the path of Esmir Bajraktarevic culminated in the ball cannoning off the shins of Sultan al-Brake and beating Abunada at his near post. Bosnia and Herzegovina were in command, Dzeko smacking a low effort against a post after reaching a clever chipped pass.

Bosnia and Herzegovina got too comfortable and allowed Qatar to reply before half-time. The 35-year-old Hassan al-Haydos, who captained Qatar on his first World Cup start, pounced on some slack defending to convert Edmílson Junior’s pullback. Qatar looked susceptible at the back but played some neat stuff going forward, none more so than in first-half stoppage time when Pedro Miguel cracked a low shot against a post. The right-back read Afif’s smart pass and after taking the ball on his right foot, with his near-perfect next touch he almost equalised.

Barbarez recognised his team had fizzled out and introduced Amar Memic and Benjamin Tahirovic at half-time. Dzeko was withdrawn to a warm ovation just after the hour as part of another double substitution. But while Demirovic almost freed Dzeko before the Schalke forward’s departure and Alajbegovic again exhibited his endearing attacking edge, darting past his marker to send in a dangerous cross from the byline, Bosnia and Herzegovina failed to box off the game. Qatar collapsed against Canada but did nothing of the sort here, Boualem Khoukhi’s volley from a rehearsed corner causing panic midway through the second half. For Bosnia and Herzegovina, a collective pang of relief when the hydration break arrived.

Bajraktarevic stung the palms of Abunada after Sead Kolasinac brilliantly transformed defence into attack and from the subsequent phase Bosnia and Herzegovina added a third, Mahmic firing in after the ball squirted free near the penalty spot. Mahmic whipped off his shirt in celebration, the knockout stage in sight.