The result was a disappointing start as captain for Manchester City striker Edin Dzeko after he took over the armband from Emir Spahic, who retired from international football following the 2014 World Cup.
Bosnia seemed to be cruising after a Vedad Ibisevic header gave them an early lead, as the home team dominated and spurned several chances in front of a passionate home crowd in Zenica.
Those near misses cost Bosnia dearly as Cristofi beat the home team’s keeper Asmir Begovic when he headed home an inviting cross from the left on the stroke of halftime.
Roared on by their fans, Bosnia laid siege to the Cyprus defence after the break but were again caught out at the other end, as Cristofi raced clear of Ermin Bicakcic and beat the advancing Begovic with a cool finish.
Bosnia wasted a golden opportunity to equalise in the 89th minute when Miralem Pjanic's weak penalty kick was saved by Antonis Giorgallides after Dzeko, who was booked several minutes earlier for dissent, was brought down.
"We didn’t deserve to win because we sat back on our 1-0 lead when we should have gone for the second,” Bosnia coach Safet Susic told the country’s BHT television.
"We didn’t create too many clear-cut chances in the second half and having missed a late penalty, we can only congratulate Cyprus."
Dzeko added: "We started well but were rattled after conceding the equaliser out of the blue. It wasn’t our night and we may rue this defeat because tougher games are coming our way."
(Writing by Zoran Milosavljevic in Belgrade; editing by Toby Davis)
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