Pat Fenlon made three changes in his quest to end decades of FAI Cup hurt for the Hoops faithful in replacing Robert Bayly, Sean O'Connor and Stephen McPhail with Shane Robinson, Ronan Finn and Gary McCabe from the side which was beaten by Cork City.
The visitors made only two changes with Kurtis Byrne and Patrick Hoban, who both scored against Derry City in the league last Monday, being benched for Donal McDermott and David McMillan.
The first chance of the game fell to the home side but they would have wished such an opening in front of goal would have fallen to anyone but central defender Jason McGuinness, who slipped with the goal gaping.
Steadily, Stephen Kenny's side settled and Shane Robinson pulled off a starring intervention to take the ball off Richie Towell's toe after a delightful Daryl Horgan cross with the winger himself then shimmying inside to curl one agonisingly outside the post for Dundalk.
On 25 minutes, the Hoops were left seething when Patrick Cregg's free kick was headed past Peter Cherrie, who was all at sea, by Karl Sheppard although the linesman judged that he did so from an offside position.
The better chances for the rest of a fairly low key opening 45 minutes fell to Dundalk and both called Barry Murphy into action as he first had to save at his near post from Horgan and then got down to his right again to keep out Towell while Sheppard was inches away from connecting with Ronan Finn's enticing cross at the other end.
For so long, the second half followed the same tentative period too, always a danger when playing cup football especially for two giants of the domestic game who have gone some time without success in this competition.
In fact it took until the 70th minute for the first chance to be created and what a chance it was.
Cherrie's quick throw released Darren Meenan who played it inside for David McMillan. His quick pass behind Conor Kenna was met by Kurtis Byrne who sent the ball around Murphy, and the upright by the slimmest of margins.
Dean Kelly and Patrick Hoban were introduced for their respective sides but the chances were still not forthcoming for either.
Late shots for subs Ryan Brennan and John Mountney were not troubling either goalkeeper although Murphy did have to be alert to tip over a swirling free kick from Horgan that was headed for the top corner from 40 yards.
That intervention means the sides will do it all again on Monday night in Louth for the replay, just five days before their EA Sports Cup final at the same venue.
Shamrock Rovers: Barry Murphy; Simon Madden, Conor Kenna, Jason McGuinness, Luke Byrne; Shane Robinson, Patrick Cregg, Ronan Finn; Kieran Marty Waters (Ciaran Kilduff 89), Karl Sheppard (Dean Kelly 66), Gary McCabe (Ryan Brennan 74).
Subs not used: Robert Cornwall, Robert Bayly, Stephen McPhail, Ciaran Kilduff, Craig Hyland (GK).
Booked: Madden (33), Robinson (45).
Dundalk FC: Peter Cherrie; Sean Gannon, Brian Gartland, Andy Boyle, Dane Massey; Chris Shields, Richie Towell; Darren Meenan (John Mountney 83), Donal McDermott (Kurtis Byrne 54), Daryl Horgan; David McMillan (Patrick Hoban 77).
Subs not used: Mark Rossiter, Ruaidhri Higgins, John Mountney, Marc Griffin, Gabriel Sava (GK).
Booked: Gannon (56), Shields (87), Hoban (93).
Man of the Match: Daryl Horgan (Dundalk).