The striker latched on to a neat pass from Derek Riordan to slam home ten minutes from the end.
But it was a game that Hamilton could have had wrapped up by half-time had they taken their chances.
Hamilton threatened first on seven minutes when James McCarthy outpaced Darren McCormack down the left, but his cut-back was taken by Grzegorz Szamotulski ahead of striker Kenny Deuchar.
A minute later, Brian Easton's throw in found McCarthy just outside the box but his long-range effort flew past the right post.
Simon Mensing played a superb ball down the right which was cleverly dummied for Paul McGowan to latch on to but Szamotulski gathered at his feet after 11 minutes.
Good work by McGowan took him into the left side of the box on 34 minutes but his cross was hooked past by Deuchar.
James Gibson's free-kick was headed into the box by Mensing but Deuchar sent another effort past the left post in 37 minutes.
But Alan O'Brien was desperately unlucky to see his effort slide just past the left post after latching on to Colin Nish's cutback from the right.
Ten minutes into the second half, McCarthy drove a pass across the box when a touch from McGowan would have put Hamilton ahead.
But Hibs took a firm grip of the game after that and on 57 minutes Riordan sent John Rankin darting down the left and his cross was headed over by Nish, who should have done better.
A minute later, Fletcher should have done better than slice wide from a position right in front of goal and with just Tomas Cerny to beat.
But Hibs were firmly on top and scored the winner after 80 minutes.
Hamilton tried to get back into the game with sub Richard Offiong looking lively but just couldn't find a way past a stubborn Hibs defence.