The Dubliners were in control for long spells, surging 2-0 clear early in the second-half before a stunning Liam Kearney volley on his debut kept the issue in doubt right to the end.
Trailing 1-0 at the interval, City introduced Kearney for the second-half, but it was the experienced Colin O'Brien who almost created the chance of an equaliser nine minutes after the re-start.
He went to ground under the challenge of goalkeeper Shay Kelly, who was then shown the yellow card for carrying the ball outside his area. City fans in the Shed screamed penalty, but to no avail.
After 58 minutes Bohs claimed a second goal which was the essence of simplicity. Jason McGuinness's long headed clearance was flicked on by Glenn Crowe for Robbie Doyle to hammer an unstoppable shot past Michael Devine for a 2-0 lead.
Kearney, signed from Nottingham Forest, produced an exciting finish by scoring with a superb volley 18 minutes from the end. It came from a headed clearance by Bohs following a corner and Kearney let rip from 25 yards with a stunning right foot shot.
Bohs gambled with the fitness of right back Damien Lynch, who played with a couple of broken fingers heavily guarded by protective bandages but didn't look unduly perturbed by his predicament.
At the opposite end City included Kevin Murray for the suspended Derek Coughlan, and Denis Behan had the unenviable task of filling John O'Flynn's shoes, partnering George O'Callaghan up front.
O'Callaghan showed up well in the opening stages as Oman found his name entering the book for a trip on the City striker after just eight minutes.
City's Kevin Doyle went close with a couple of shots before Bohs struck for the crunch opening goal. He swept into the area with a diagonal run and his low strike skidded across the top of the surface, and just wide of the far post after 13 minutes, following an impressive break-out from defence, initiated by Murray.
Doyle was again prominent 17 minutes later, when he picked up the ball in a central position and once more dribbled past a couple of defenders before drilling another daisy cutter which just skimmed past the far upright. The champions took the lead out of the blue Robbie Doyle shipped a hefty challenge from behind, but referee Paul McKeon played the advantage and Fergal Harkin had the presence of mind to fire in a cross from the right which Dave Morrison finished with aplomb from close range.
Within a couple of minutes Devine had to scramble to his left to deflect a tricky shot from Kevin Hunt away for a corner and City's frustration became evident, when Behan was shown the yellow card for a robust challenge on a visiting defender. They were fortunate to be only two down at the interval after Doyle wasted a glorious opportunity in first-half stoppage time.
Harkin was once again the architect, picking out the centre-forward with a precise pass, but Doyle failed to get over the ball properly and the shot went high and wide, to the right of Devine's goal.
As City pressed for an equaliser, Morrison crashed a powerful shot off an upright in a rare Bohemians attack in stoppage time before holding out for a crucial set of points.
CORK CITY: Devine; Horgan, D Murray, K Murray, Woods; Doyle, O'Brien, O'Halloran, Casey; O'Callaghan, Behan. Subs: Kearney for Casey, half-time; CP O'Brien for Behan and Bennett for Horgan, both 70 mins.
BOHEMIANS: Kelly; Lynch, McGuinness, Oman, Webb; Harkin, Hunt, Caffrey, Morrison; Crowe, Doyle. Subs: Keegan for Doyle 74 mins
Referee: P McKeown (Dublin)