A first-half header from Diane Caldwell was added to by a Katie McCabe free-kick and a tidy finish from Denise O'Sullivan as Vera Pauw's side maintained their unbeaten run.
Montenegro were reduced to 10 players late in the second half but by that stage Ireland were dominant and a second win over the same opponent in this qualifying campaign was later secured.
However, not everything fell for Ireland early on with Ruesha Littlejohn, Rianna Jarrett, Clare Shine and O'Sullivan all going close before Caldwell netted her third senior international goal.
The Dublin native bravely headed in after meeting a Louise Quinn connection following a lofted free-kick from McCabe. It was a similar set-piece from which they profited in the home win over Greece.
Ireland kept on pressing - registering a total of 18 attempts on goal - and Jarrett thought that she had doubled their lead on 50 minutes but her effort was hooked off the goal line.
Montenegro's Darija Djukic picked up a second yellow card for a foul on substitute Kyra Carusa and then McCabe stepped up with a stunning finish from a direct free-kick on 83 minutes.
O'Sullivan added some gloss to the scoreline when she combined well with Jarrett to fire in on 85 minutes. And that was that - a fourth win of the qualifying campaign.
With three games left to play - twice against Germany, once against Ukraine - Ireland remain firmly on course to be in the mix for qualification to the 2021 EURO finals.
Montenegro: Cabarkapa; Popovic, Saranovic, Bozic, Djukic; Bulatovic; Kuc (Vujadinovic 87), Karlicic, Djokovic, Stanovic (Toskovic 73); Desic (Nedic 90).
Republic of Ireland: Brosnan; Caldwell, Quinn, Scott; O’Sullivan, Fahey; O’Gorman, Littlejohn, McCabe; Shine (Carusa 58), Jarrett (Barrett 87).
Referee: Maria Marotta (Italy).