Town almost made the perfect start. Toni-Anne Wayne's dangerous delivery found Natasha Thomas, who spotted the run of Jac Ball before playing her in, but the full-back was denied by the crossbar.
Zoe Cossey was once again proving to be the main threat for the Blues and it wasn't long before she made her presence felt. The mercurial winger was cursing her luck after gliding past four Norwich defenders but her driven effort dropped down off the crossbar with City keeper Hope Armstrong well beaten.
Ipswich failed to take advantage of their early dominance and soon found themselves behind against the run of play after a stunning strike. Cook picked the ball up left of centre and with no Town players closing her down, she unleashed a terrific curling effort into the top right corner from twenty-yards.
The Blues should have drawn level in the latter stages of the half but some miraculous goalkeeping heroics from Armstrong denied both debutant Amy Nash's initial shot and Thomas' close-range rebound.
Town got off to the worst possible start after the break as the Canaries doubled their lead through half-time substitute Garrett. The tall City forward broke into the Town area after pouncing on a loose ball before finding the back of the net despite the best efforts of Town keeper Sian Fagg and covering defender Harriet Petley.
Ipswich began to become frustrated as the hosts started to gain total control of the game, with many of the Blues' attempts on goal failing to test Armstrong.
The Canaries had a great chance to put the game to bed with twenty minutes to go but substitute Christina Papadopolou was denied excellently down to her right by Fagg.
However, in the final minutes of the game, Norwich did wrap the game up as Cook netted her second of the night after bursting into the area and firing across Fagg into the far corner.
Town XI: Fagg (C), Moore, Cage, Petley, Ball, Arnoup, Craddock (Wakefield), Nash (Welton), Cossey (Box), Thomas, Wayne.
Unused: Clarke, Flatt