Jets midfielder Nicola Bolger had put the visitors ahead against the run of play eight minutes before the break, but Taylor equalised and then found a 65th-minute winner.
Victory, coming off a loss to the Brisbane Roar, dominated the early exchanges and Barbieri was called into action six minutes in, producing a strong save to deny Taylor.
The impressive Taylor thought she had made it 1-0 on 15 minutes when she tapped in a Caitlin Friend cutback, but the offside flag denied Victory the lead.
Vicki Linton's team continued to push, but it was the Jets who took an unlikely lead in the 37th minute.
The lively Lisa de Vanna fed Bolger into the area, and she buried her shot into the top corner and to goalkeeper Brianna Davey's right.
Victory needed just four minutes to equalise as Katrina Gorry's well-weighted through ball found Taylor, who composed herself before placing past Barbieri and into the bottom corner to send her team into the break on level terms.
De Vanna had two penalty shouts turned down just before the hour-mark, while Gorry should have done better in a one-on-one chance with Barbieri.
Taylor completed her double and struck what proved to be the winner after an error from Jets defender Alexandra Huynh.
Huynh stumbled as she tried to nod Davey's long ball back to Barbieri, and although Taylor was initially denied by the shot-stopper, she pounced on the loose ball to tap into an empty net for her fourth goal of the campaign.
Teenage Victory goalkeeper Davey, who was chosen ahead of Barbieri in the pre-season, was forced into action on several occasions late in the encounter, but the hosts deservedly held on for three points.
Melbourne Victory 2 (Jodie Taylor 40, 65)
Newcastle Jets 1 (Nicole Bolger 36)
Saturday 3 December 2011
Skilled Stadium, Geelong
Local kick-off: 3pm
Referee: Catherine Hoffman
Melbourne Victory: Brianna DAVEY (gk), Rebekah STOTT, Maika RUYTER-HOOLEY, Kendall FLETCHER, Danielle JOHNSON, Stephanie CATLEY, Ashley BROWN (Louisa BISBY 61), Jodie TAYLOR, Catlin FRIEND (Laura SPIRANOVIC 84), Katrina GORRY, Amy JACKSON
Substitutes not used: Cassandra DIMOVSKI (gk), Gulcan KOCA
Yellow Cards: Amy Jackson 23’
Red Cards: Nil
Newcastle Jets: Melissa BARBIERI (gk), Hannah BREWER, Alanna KENNEDY, Alexandra HUYNH (Tara ANDREWS 84), Nicola BOLGER, Gema SIMON (Bronte BATES 78), Linda O'NEILL (Rhali DOBSON 70), Lisa DE VANNA, Monnique KOFOED, Stacey DAY, Ariane HINGST