Megan Connolly gave the hosts the lead after three minutes, Aine O’Gorman’s pull back across the box found Stephanie Roche.
Roche’s shot was blocked by Montenegro keeper Obradovic with her foot, Megan Connolly was on hand to slot the ball into an empty net.
Aine O’Gorman doubled the lead on the 11th minute with a speculative left footed effort from the edge of the box which curled in behind the post.
Armisa Kuc rattled the cross bar on 14 minutes, heading a corner off the top of Emma Byrne goal.
Ireland came close to extending their lead on 23 minutes, Obradovic kept out Karen Duggan shot, Megan Connolly’s follow up header was straight at the keeper.
Stephanie Roche landed an exquisite free kick in the final minute of the first half. Roche left footed free left Montenegro keeper Obradovic flat footed.
Ireland picked up where they left off after the break Julie-Ann Russell unlucky not to add to the score on 47 minutes her left footed curler just wide of the far post.
Aine O’Gorman made it 4-0 eight minutes into the second half. Katie McCabe’s free kick found Stephanie Roche who headed the ball into O’Gorman’s path to blast home.
O’Gorman sealed her hat-trick on 58 minutes with a super strike from 30 yards which gave Montenegro keeper Obradovic no chance.
Louise Quinn made it 6-0 on 62 minutes heading Jule-Anne Russell’s corner home. Stephanie Roche made it seven three minutes later.
The referee waved play on after Katie McCabe was fouled in the box, Roche drove into the bottom left corner of the net.
Roche completed her hat-trick on 68 minutes with a deftly header, heading McCabe’s cross past the stranded Obradovic.
Fiona O’Sullivan made it 9-0 heading home Julie-Ann Russell’s cross with seven minutes remaining.
The final score is a joint record score the Republic of Ireland WNT having previously beaten Malta 9-0 away in 2003.
Republic Of Ireland: Emma Byrne, Sophie Perry, Louise Quinn, Savannah McCarthy, Meabh De Burca, Aine O’Gorman (Fiona O’Sullivan 77), Megan Connolly(Katie McCabe HT, Karen Duggan, Ruesha Littlejohn (Denise O’Sullivan 63), Juile-Ann Russell, Stephanie Roche
Substitute’s not used: Grace Moloney, Jetta Berrill, Diane Caldwell, Emma Hansberry
Montenegro: Obradovic, Radanovic, Rondovic, Trutic, Djurkovic (Bozic 78), Djukic, Kuc, Vulic, Bulatovic, Bojat, Djokovic (Zlaticanin)
Substitutes not used: Cadjenovic, Vesovic, Radunovic, Popovic
Referee: Ivana Projkovska (Macedonia)