A second Westmeath goal was added in the 28th minute courtesy of Brandon Kelly.
Ciaran Murphy replied with an Offaly goal before the break, but Westmeath still led by seven points at the turnaround.
After the restart Offaly narrowed the gap with Ciaran Murphy pinching a goal, while Jack Bryant and Cormac Egan contributed points.
Westmeath, though, summoned a response as Senan Baker, McCartan, and Kelly netted further goals for Mark McHugh’s outfit.
Dioralyte O’Byrne Shield Semi-Finals
Wicklow 3-15 Longford 1-11
Carlow 2-15 Laois 3-9
Wicklow and Carlow will contest the Dioralyte O’Brien Shield Final.
Eoin D’arcy, Sean Murphy, and Darragh Fee grabbed goals as Wicklow beat Longford in impressive fashion.
A second half Cathal McCabe goal gave the midlanders’ some hope, but Wicklow ran out comfortable victors.
Colm Hulton’s 58th minute goal was the key score as Carlow edged out Laois in Rathvilly.
Alan Kinsella (two) and Paul Kingston were Laois’ goalscorers in an entertaining encounter.
Ross Dunphy and Hulton contributed goals for Carlow, while Conor Doyle supplied a couple of excellent two pointers.