Paul Hanlon and Jason Cummings were on the scoresheet for Hibs while Mitchel Megginson had equalised for the home side.
Chris Turner was dismissed on the hour mark for violent conduct, minutes before Cummings’ winner. And the visitors will feel it was a deserved victory after carving out most of the chances.
They made a confident start with Cummings lashing the ball wide of the target from the edge of the box while Farid El Alagui got on the end of Martin Boyle’s cross but could not keep his effort on target.
Their dominance was rewarded on 36 minutes when they were awarded a penalty but El Alagui’s spot-kick struck the post and rolled across the line before being hacked away.
But they made amends seven minutes later when Scott Allan’s cross was nodded in by Paul Hanlon to make it 1-0.
Sons’ best chances of the half fell to Scott Agnew, whose free-kick was well saved by Mark Oxley, while the keeper was again on hand to keep out Mark Gilhaney’s effort.
Hibs continued to press after the break with El Alagui’s shot blocked while Allan’s attempt was saved from the resulting corner.
But Dumbarton grew in confidence and went close when Scott Taggart jinked past three players but his low shot was saved by Oxley.
And the hosts equalised on 55 minutes when Oxley could only parry Taggart’s shot and Megginson slotted in the rebound.
The home side’s chances of victory were dashed on the hour mark when Turner was sent off for violent conduct after a crunching challenge on Jordan Forster.
And Hibs made them pay by regaining the lead on 66 minutes when Cummings thumped the ball in from inside the box.
The visitors should have wrapped the game up with El Alagui shooting narrowly wide with the goal at his mercy while Boyle fired an effort just wide.
And in the dying stages Dominique Malonga’s low effort hit the post before being cleared.
But it did not matter as they held on for an away victory which moves them ahead of Rangers on goal difference, who have two games in hand, while Dumbarton remain seventh.