Sean Gannon scored a scrappy late, late winner to deprive Longford Town of a creditable draw at Tallaght Stadium.
With the sides having swapped penalties early in each half, champions Rovers late pressure told three minutes into added time.
Dylan Watts’s free kick was half cleared to Gannon whose drive deflected to the net off Longford captain Aodh Dervin.
The result was tough on Longford, if the performance was encouraging following last week’s 4-0 home humbling by Drogheda United.
With four changes to the side, Longford had the ideal start of the lead goal seven minutes in.
Striker Aaron Dobbs pounced as Rovers’ defender Roberto Lopes dallied to win a penalty against the back-tracking Cape Verde international.
Lopes was booked before Dylan Grimes confidently sent Alan Mannus the wrong way from 12 yards.
Though enjoying plenty of the ball, and forcing four corners in relatively quick succession, sluggish Rovers’ probings came to nothing as Longford’s work-rate was impressive.
Rovers brought in Gary O’Neill and Rory Gaffney at half-time, adding much improved tempo from the home side as they worked Michael Kelly twice inside a minute.
Chris McCann initially forced a corner from the diving Kelly before the Town keeper was there again to save a Burke header at the near post from Danny Mandroiu’s corner.
The pressure of Rovers’ eighth corner finally told on 54 minutes, though.
Remarkably, it was a reverse of the game’s first penalty incident as Dobbs hauled down Lopes as he darted across the area to meet Burke’s quickly taken corner.
Burked drilled the resulting spot kick down the middle to level the game.
Rovers struggled to create much as they pressed for a winner.
Gaffney shot narrowly wide while Burke volleyed over the crossbar before Gannon's last gasp intervention delivered the points.
Shamrock Rovers: Mannus; Grace (O’Neill, h-t), Lopes, Scales; Finn (Gaffney, h-t), McCann; Gannon, Mandroiu (Watts, 58), Kavanagh; Burke, Greene.
Longford Town: Kelly; Chambers, O’Driscoll, Gorman, Kirk; Bolger (Verdon, 72), Dervin; Elworthy, Robinson, Grimes; Dobbs (R. Manley, 80).
Referee: Rob Hennessy (Dublin)