The game started a tad edgy as both sides attempted to figure each other out, however, Town dominated the early possession and looked to get their noses in front early.
After twenty minutes the deadlock was broken in sensational style as England Under 18 international Peake stepped up for a free-kick 20-yards from goal and found the top corner with a stunning strike to give the Blues the lead.
Roared on by the crowd, the Tractor Girls took control of the game and continued to create chances. The Blues did have the ball in the net for a second time in the first-half but after Eloise King's shot was pushed onto the post by City goalkeeper Hope Armstrong, Amanda Crump's follow up was ruled out for offside.
Town would have one final chance to extend their lead going into the break but after drifting in from the left and letting fly, Sophie Peskett was denied by the crossbar.
The Tractor Girls picked up exactly where they left off after the restart and doubled their advantage just four minutes later. After some wizardry from Peskett, the teenage Town winger laid the ball into the path of Thomas, who touched inside and found the bottom corner with a clinical effort.
The Canaries soon got themselves back into the game completely against the run of play as Aimee Durrant whipped a cross in for Garrett, who towered high to power her header towards goal but despite what looked like an initial save from Nikita Runnacles, the ball was adjudged to have crossed the line.
The Norwich response didn't phase Town in the slightest and the two-goal cushion was soon restored as the Blues were awarded a penalty. Substitute Biggs burst into the area and was hauled to the floor, with referee Reg Barker not hesitating to point to the spot. Peake stepped up in front of an incredibly vocal section of Ipswich fans and smashed her penalty into the top-left corner.
Biggs' introduction was paying dividends for the Tractor Girls and the 16-year-old was unlucky not the get on the scoresheet after an incredible solo effort. However, she didn't have to wait much longer for her first Ipswich Town goal as in the final moments of the game, she added a fourth for the Blues in sensational style.
After receiving the ball just outside the area, Biggs cut inside before curling an unstoppable strike into the top corner to cap off an unforgettable night for the Tractor Girls.
The result sees Joe Sheehan's side remain unbeaten in the league and rise to second in the Women's National League Division One South East table.
The Tractor Girls return to league action this Sunday at home to Actonians at the Goldstar Ground, Felixstowe. Kickoff 2pm.
Town: Runnacles (GK), Pannifer, Peake, Egan, Hubbard, Wilson, Crump (c), King (Wakefield), Cossey, Peskett, Thomas (Biggs).
Unused: Clarke (GK), Abrehart, Cooper