Bruce Springsteen was belting out the tunes across town but Trevor Clarke was ‘The Boss’ in Tallaght with the hit that mattered.
The wing-back pounced in the 57th minute for his third goal in four games and set the champions on their way to derby glory before Rory Gaffney sealed it late on.
But Bohs were crying foul as they felt they should have been awarded a penalty just before Gaffney’s clincher, when Dan Cleary clipped Jonathan Afolabi in the box.
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Manager Declan Devine and his staff were apoplectic, and remonstrated with fourth official Neil Doyle while Afolabi raced to confront the assistant referee.
But while replays suggested they had a case, Rovers paid no heed and punished them in the most ruthless fashion by doubling Clarke’s lead with Gaffney’s headed finish.
Clarke had shipped dog’s abuse from the Bohs fans throughout this clash played in front of a record league crowd for the venue of 7,864.
And he enjoyed milking the celebration as he raced back towards them with ears cupped, delivering again having been brought back to the club to replace free-scoring Andy Lyons.
Bohs were the standout story of this season's first series of games and while they still lead by a point, Rovers have left nobody in any doubt that they are coming for them.
Stephen Bradley’s charges started like a team on a mission and they left Bohs in a spin under a barrage of attacks - even if clear cut chances were lacking.
Gypsies centre-back Kacper Radkowski had a torrid time in those opening minutes, twice responsible for Rovers best chances in that spell.
First, Johnny Kenny robbed him at the endline to tee up Richie Towell, whose angled shot was saved by James Talbot at the near post.
And moments later, Kenny outmuscled the big Pole for a second time but couldn’t get enough bend his low shot - from Cleary’s ball up the line - to beat Talbot.
That direct route to Kenny was always a useful outball when the more patient approach failed to yield dividends.
Towell appealed for a penalty after going down under a Talbot challenge when trying to connect with Jack Byrne’s through ball.
Referee Rob Hennessy deemed Towell to be offside, although replays suggested he wasn’t. Still, the Hoop ace - scorer of a cracker in Derry on Monday - went down easily.
Up to then, Bohs had offered nothing. They struggled for time on the ball and the sight of Declan Devine turning to his bench and puffing out his cheeks told a story.
But they eventually settled into proceedings and Jordan Flores’ free-kick that zipped just wide of Leon Pohl’s far post was a good settler and they improved thereafter.
Still, Rovers remained the dominant and more adventurous side.
Towell was like a Tasmanian Devil, haring around the place but he snatched at one shot that fizzed wide when Neil Farrugia was arguably better placed to execute.
And Clarke was frustrated after snatching at a shot that failed to trouble Talbot, having capitalised with a menacing and unchecked run into the box.
But while Bohs lacked quality in aspects of their play, they were becoming more of a threat and forced Pohls to make the save of the half.
Dylan Connolly could have picked out Ali Coote, who made a good run into space but picked out Grant Horton instead.
And the right-back pulled a dangerous ball across the box for the other full-back, Paddy Kirk, who had initiated the whole move with a booming switch off the other flank.
In the box, Kirk took a touch and brought the best out of Pohls - deputising for the injured Alan Mannus for the foreseeable - from 10-yards.
But rather than galvanise Bohs, it merely refocused Rovers and they took a decisive lead approaching the hour mark.
Talbot had only just swatted away a Kenny drive towards the top corner when he kept out the striker’s header - from Farrugia’s cross - with a brilliant save down low.
But he could do nothing about the loose ball bobbling around, inches from his grasp, as Clarke pounced to smash home and in front of the South Stand.
Byrne curled wide soon after while Declan McDaid wasn’t far off turning in a Connolly cross at the other end.
But Bohs were up in arms with 13 minutes to play when Afolabi went down under that Cleary challenge. The Rovers centre-back was at full stretch but didn’t get the ball.
The Gypsies' frustration was merited but ultimately fell on deaf ears as the four-in-a-row chasing Hoops drove home their advantage five minutes later.
Graham Burke combined with Farrugia down the left and Burke’s shot was blocked by Bohs skipper Keith Buckley, but it looped up for Gaffney to head home.
Bohs continue to set the pace, but Rovers’ slow start to the season looks a distant memory now because the champions are motoring.
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