Despite dominating the remainder of the half, the hosts fell behind again, to a controversial penalty when skipper Luke Byrne tangled with Junior in the area.
Referee John McLoughlin had no hesitancy pointing to the spot, and Dawson Devoy netted his third penalty in three games, smashing down the middle.
The visitors came flying out of the traps following the restart and extended their lead thanks to a cool finish from Kris Twardek.
The Canadian winger cut inside on his left foot leaving the defender in his wake, having been slipped in on goal by Ali Coote, and slotted past the onrushing Clarke to make it 3-1.
Bohs still had the bitter taste of what felt like a defeat on Friday night, having thrown away yet another two late points at home this time to nine-men Finn Harps in a dramatic draw, but showed no ill-effects as they put together a classy performance in a hostile atmosphere.
The visitors took the lead shortly after when pacy winger Burt cut inside from the left wing, and despite a couple of Shels defenders trying to haul him down, showed incredible balance and skill to stay on his feet and got his reward seeing his strike deflect off Shane Griffin and past the helpless Brendan Clarke.
Goals from Liam Burt, Dawson Devoy, Kris Twardek and Junior Ogedi-Uzokwe condemned Damien Duff’s side to another home game without victory.metasports
The slick surface, impacted by heavy showers, made it ideal conditions for quick football and full blooded challenges and having notched just the one point in front of their vocal home support, Shels came into the clash full of confidence having inflicted Derry City’s first defeat of the season with an excellent 2-1 away win.