You'll never beat the Irish. The chorus from the Republic of Ireland squad's chart-topping Euro 2012 single has the capacity to grate but their ability to churn out results under Giovanni Trapattoni is a source of pride and encouragement.

They signed off in front of their home supporters for the finals in Poland and Ukraine with a performance that got better as the minutes ticked by and a victory that prolonged their impressive sequence. It is now 13 matches without defeat, with only three goals having been conceded in the run.

Ireland fly to Italy on Sunday morning to continue their preparations at a week-long training camp before they play a final warm-up fixture against Hungary in Budapest on Monday week. They will arrive in Poland with their minds focused and their confidence high.

Who says that Trapattoni's braves cannot upset the odds, despite being pitched into a group with Croatia, Spain and Italy? Certainly, nobody within their ranks. The crowd rose to acclaim them with ten minutes of this game to go, by which time the substitute Shane Long had headed what proved to be the winning goal. The margin of victory would have been greater but for the woodwork and some fine saves from the Bosnia goalkeeper Asmir Begovic.

There were plenty of positives, not least James McClean's vibrant full debut. There were no nerves from the Sunderland left winger, who was switched to the right for a spell at the beginning of the second-half, only pace, tricks and a pleasing directness. His swashbuckling style creates a buzz. Although he tired in the second period, he received warm praise from Trapattoni. He will feel more of a part of it now.

McClean was eclipsed, though, by Aiden McGeady, who came on as a half-time substitute to lay on the goal and take centre stage in a clutch of other openings. It was quite a way for the Spartak Moscow winger to respond to criticism about his form from Roy Keane, the former Ireland captain.

Trapattoni could also take heart from the impact of his two replacement strikers, Long and Jon Walters. There was an argument to be had that Ireland looked more threatening with the pair in tandem. Trapattoni and the players completed a lap of the pitch at full-time to thank the fans for their support.

The feel-good factor is unmistakeable. Opponents dare not underestimate Ireland.

Trapattoni made six substitutions, as he sought to promote the fitness of as many players as possible but he still wanted a result and it was clear that Bosnia, who fell in the Euro 2012 play-offs to Portugal, represented a test.

They were the better team for much of the first-half, moving the ball fluently and with the captain Zvjezdan Misimovic to the fore, from his roaming role on the left. Edin Dzeko flickered and Miralem Pjanic threatened from distance. Bosnia, though, were let down by their end product.

Ireland had the clearest first-half chance, in the 45th minute, when Robbie Keane flicked through for Damien Duff, who was denied at close-quarters by Begovic and McClean had the supporters out of their seats. He cut inside two blue shirts to create a shooting chance for the impressive Darron Gibson, which he snatched at and McClean also forced Begovic to turn behind at the near post.

Ireland felt that they should have had a penalty when Glenn Whelan burst into the area in the 13th minute and rounded Begovic only to be taken down by the goalkeeper. Whelan's touch was heavy but Begovic was nowhere near the ball and there was contact with the Ireland midfielder.

The second-half brought the slew of substitutions but McGeady settled immediately, with first touch nearly bringing the breakthrough. Kevin Doyle rose to meet Stephen Ward's free-kick and McGeady stretched to direct a volley goalwards. The shot hit the post, with Begovic beaten.

Ireland were superior in the second period and McGeady was at the heart of everything. It was from his right-wing cross that Walters ought to have scored. Having timed his run, the striker rose unchallenged but he could only head against the crossbar. Such chances will have to be taken in Poland.

It did not matter here and the goal owed everything to McGeady's ingenuity. Having burst onto a ball up the inside right channel, he checked inside Senad Lulic to cross with his left foot. When Long went up at the far post, it was clear that he was not going to miss.

McGeady fed Walters for another clear chance that Begovic repelled – he refused to be beaten by his Stoke City teammate – and, although the Bosnia substitute Mehmed Alispahic spurned a glorious opportunity to equalise, Ireland finished on the front foot when Begovic brilliantly saved Long's header from McGeady's cross and Keith Andrews nodded the follow-up off target.