Delany first thwarted Keith Fahey in the first half before making terrific reaction saves from Ryan Brennan and Marty Waters in the second.
Danny North then almost snatched it for Rovers at the death but headed over the crossbar.
The Rovers Ultras unfurled a banner before kick-off proclaiming “One Club Runs This City”.
It certainly didn’t faze Bohemians with Long having said after their home defeat to champions Dundalk on Tuesday that nobody at the club was feeling sorry for themselves and that they’d arrive in Tallaght with a “spring in their step”.
His side, with 18-year-old Stephen Best in at centre-half for the suspended Anto Murphy, duly shaded a fast and furious opening which saw a booking on five minutes for Hoops’ Dave Webster over a foul on Keith Buckley.
Bohemians winger Paddy Kavanagh then had the first sight of goal on 10 minutes when drilling into the side-netting following a weak headed clearance from skipper Derek Pender’s long throw.
Rovers soon took a grip on the game, enjoying a fair deal of possession throughout the remainder of the half, though they struggled to pose a threat to Delany’s goal until half-time approached.
Webster was unmarked to head over from a Sean O’Connor free kick on 37 minutes before Delany was finally called into action three minutes later.
Gary McCabe fed Keith Fahey, with the ex-Ireland international bursting past a defender to get in on goal. Delaney was out sharply to save bravely at the feet of the Rovers midfielder.
Rovers had a let-off at the other end two minutes later with the dynamic Webster getting in a vital block to thwart a Dean Kelly shot.
There was added impetus to Rovers on the resumption with Fahey’s weak effort comfortable for Delany before David O’Connor headed wide from a Fahey corner.
In replicating the first half, Rovers struggled initially to create serious chances.
That changed, however, in the final quarter as Delany came into his own to excel.
First Ryan Brennan’s header brought a brilliant reaction save from Delaney after fellow substitute Mary Waters’ left-wing cross on 78 minutes.
A minute later, Delany was there again to make an equally terrific stop from Waters in a goalmouth scramble.
Rovers maintained the pressure into stoppage time but couldn’t find a way to goal.
Danny North was inches away from winning it right on 90 minutes, but looped his header over the top.
Hyland; Madden, Kenna, Webster, D. O’Connor; Cregg; S. O‘Connor (Waters, 71), Fahey, McPhail (R. Brennan, 61), McCabe (North, 85); Drennan.
Delany; Pender, Prendergast, Best, Fitzgerald; Kavanagh, Lopes, Creevy, Evans (Moore, 75); Buckley (Dillon, 61); Kelly (Byrne, 79).
Paul Tuite (Dublin).