The decisive moment arrived just 80 seconds into the second half when defender Durnan smashed the ball home from 10 yards.
The visitors had also travelled to Edinbuirgh on the back of successive defeats but this well-deserved three points boosts their chances of securing a play-off spot in the Scottish Championship.
Hibs certainly finished the game stronger but were unable to fashion an equaliser during the final 20 minutes.
Dominique Malonga twice had efforts for the beleaguered hosts, first firing wide from outside the box before having a 12-yard header saved.
Franck Dja Djedje went close in the 84th minute while, at the other end, Stephen McKenna had a shot for the Doonhammers.
In a goalless first half, Queen of the South dominated the early stages with Kevin Holt going close twice during the opening six minutes after Gavin Reilly had missed inside 40 seconds.
The hosts improved as the half continued with Malonga having a close-range header blocked on 34, although visiting striker Derek Lyle had an effort saved by Mark Oxley shortly afterwards.
Although Hibs remain second in the table, their nearest challengers Rangers are level on points with two games in hands. The Gers welcome champions Hearts to Ibrox on Sunday.