Netherlands forward Vivianne Miedema scored in each half before a late Mollie Green goal cut the deficit for the visitors.
Montemurro - who has been linked with the vacant Matildas job after the sacking of Alen Stajcic - has guided Arsenal to second in the Women's Super League and his side will now face Manchester City, who beat league champions and FA Cup holders Chelsea 2-0, in the final.
City are aiming to lift the League Cup trophy for a third time after triumphs in 2014 and 2016. The final is on February 23.
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