Franck Dja Djedje opened the scoring and Dominique Malonga netted either side of half-time to give Hibs the win.
Hibs started on the front foot but struggled to break through a well-organised Dumbarton defence.
The game’s first big chance came on 24 minutes when Malonga slipped in Dja Djedje but the striker failed to make a clean connection allowing Danny Rogers to gather.
Dja Djedje made amends for that miss five minutes later when he brought down a Keith Watson cross in the box before turning and firing into the net from 12 yards.
The hosts doubled their lead soon after and Watson was again the provider as he crossed for Malonga to head home.
Malonga got his second of the game on 55 minutes when he slotted home from close range after a clever lay-off from Scott Robertson.
Dja Djedje came close to getting his second on 73 minutes after terrific play from Fraser Fyvie but Mark Wilson made a last-gasp challenge to deny him.
Rogers came to Dumbarton’s rescue soon after as he managed to beat away a vicious strike from Dja Djedje on the angle and the game ended with a comfortable win for Hibs.
The win lifts them above Rangers into second in the table but the Gers, who are two points behind them, have three games in hand, while Dumbarton stay seventh.