Caitlin Morris bundled home at the back post on 110 minutes to hand the visitors a 2-1 third round south-coast derby triumph in a hard-fought contest between the Women's National League Southern Premier Division rivals.
Earlier, Cherelle Khassal had fired the Blues ahead with a smart, looping finish on 31 minutes before Lucia Kendell's leveller after 65 minutes sent the tie into extra-time.
After a cagey opening, Khassal was sent racing away but fired straight at Kayla Rendell with what was the first time either goalkeeper had been tested on 20 minutes.
It was Khassal who broke the deadlock 11 minutes later as her looping effort from just inside the area beat Rendell.
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Shannon Albuery then saw a glancing header tipped over the crossbar by Rendell soon after as the Blues went in search of a second.
Pompey were up in arms when Sammy Quayle went down after a challenge from Leeta Rutherford in the area but referee Justyn Leonard waved away the hosts' appeals for a penalty.
The Blues withstood some pressure early in the second half, yet Southampton drew level after 65 minutes when Kendall headed home Shelly Provan's pinpoint cross.
Pompey were wondering how they did not restore their advantage on 73 minutes. Goalkeeper Rendell spilled the ball after an Ava Rowbotham free-kick with full-back Milly Mott superbly clearing two attempts on the goalline – although the hosts were arguing Mott had used her hand.
Caitlin Morris then dealt Pompey a hammer blow five minutes into the second half of extra-time, bundling home at the back post with the hosts unable to clear the danger. Pompey kept pushing until the end but there was no way through as they suffered defeat.
Pompey Women: Haughton; Rowe, Gotch, Gane, Bridge, Rowbotham, Jones, Lane, Quayle, Albuery, Khassal. Subs: McDonnell (Quayle, 83), Tonks (Jones, 98), Younger (Rowbotham, 112), Kingshott, Cleeve, Laidlaw, Waters, Aldridge, Stroe