Goals from Stephen Caffrey, Bobby Ryan and Glen Crowe ensured the victory for the Dublin club in an entertaining game in which the result hardly flattered them.
From the first minute, they were the dominant side with goalkeeper Seamus Kelly left as an interested spectator for much of the night.
Robbie Doyle headed wastefully over in the 31st minute but six minutes later, Bohemians did take the lead when Damien Lynch took a quick throw to Ryan on the right and his low cross was stabbed home at the near post by Stephen Caffrey.
From then on, it was all Bohemians. Doyle had a header blocked by Baha while also blazing a shot well wide with Crowe and Mark Rutherford screaming for the ball in the box, Rutherford also flashed a shot well wide after bursting through before Ryan gave the eircom League champions the aggregate lead on the stroke of half time.
Once more the goal was manufactured on the wing this time the left as Crowe's deft lay off released Doyle who burst into the box before sending over a perfect low cross for Ryan to race in at the far post and convert.
And in the 58th minute, Crowe made the result safe with a wonderful third goal when he placed a superb volley past goalkeeper Yuri Zhaunou after Rutherford and Doyle had combined on the left wing to create the chance.
In the remaining 32 minutes Bohs had a number of other chances with Crowe flashing a shot across the face of goal and substitute Fergal Harkin heading inches over from a Ryan corner and the missed chances did not prove costly for the Dublin club.