Ellen Dolan struck early in the first half to give the Peas the lead in Belarus.
Peamount United have won their opening Women's Champions League qualifier in Croatia.
They beat Dinamo Minsk 2-1 after extra-time.
Kerri Letmon scoring the winner in the 95th minute.
Ex-Mucklagh forward, Ellen Dolan scored for the Premier Division champions in the sixth minute but the Belarusians equalised just after the half-hour mark.
That marks Dolan's 11th goal in all competitions this season.
While Westmeath's Lucy McCartan lined up for the Dublin side in defence.
The Peas will play the winners of Osijek versus Myjava.
There Are Very Strict Rules When It Comes To International Sport - Tanaiste
Westmeath SFC: Great To Win At The Weekend - John Heslin
2027 Irish Open To Take Place Next July
Offaly’s First All-Ireland Winning Hurling Manager Andy Gallagher Dies Aged 89
Laois SFC: Killeshin Deliver Knockout Blow To Portlaoise
Westmeath SFC: Moate All Whites Turn Attention To County "Standard Bearers"
Town Continue Rich Vein Of Form With Creditable Students Draw
Offaly SFC: Shamrocks And Tullamore Secure Semi-Final Spots
John Heslin Aiming To Feature For Westmeath Next Season
Westmeath SFC: St Loman's Mullingar And Moate All Whites Progress
Athlone Town Move Closer To Women's Premier Division Title
Alex Dunne Keeps F2 Title Hopes Alive With Spanish GP Podium
Trump To Lift US Tariff On Irish Whiskey After Talks With Shane Lowry
Lowry Breaks Title Drought With Magnificent Irish Open Victory
Shane Lowry Leading The Way At The Irish Open
Alex Dunne Secures Front Row Start For F2 Feature Race In Madrid
Former Golf Coach Stunned With Stuart Grehan Not Competing At Irish Open
Treaty United The Next Test For Athlone Town