Ibrahimovic finished off from close range in time added on after halftime substitute David Beckham chippedthekeeper, denying the veteran Englishman his first goal since signing in January.
As Hamilton pressed for an equaliser Smith did well to block Mark McLaughlin's close-range volley from Lyle's free-kick and, as half-time approached, Shaun Hutchinson cleared the ball off the goal-line after Lyle had chippedthekeeper.
On 19 minutes Bellamy played a one-two with Gareth Bale and hared away towards the Polish goal, only for the covering Michal Zewlakow to clear the danger as Bellamy chipped over onrushing keeper Lukasz Fabianski.