Frustration was starting to build among the Cup favourites before Josh Brillante's vital equaliser.
Defeat will be tough to take for Wellington but it's been a memorable Cup adventure. After winning just one FFA Cup game across six seasons, they were one game away from reaching the club's first final.
Coach Ufuk Talay brought in 18-year-old defender Finn Surman for Tim Payne, while Nick Pennington replaced Clayton Lewis, with the two senior men on All Whites duty.
The first half took a while to get going. The Phoenix were content to sit in a deep block, allowing the Victory to play in front of them, without too many threatening moments.
Marco Rojas looked lively but the youthful Wellington back four held their structure, with Alex Rufer dropping deeper in possession.
There were few opportunities, as the Victory couldn't find the final ball. Hooper just failed to connect with David Ball's cross — from six yards out — as Reno Piscopo and Gael Sandoval started to become more influential, after a quiet start, while Victory defender Roderick Miranda went close with a near-post header.
When the Phoenix goal came in the 39th minute, it was a beauty. After sustained possession, Piscopo's one-touch pass split the Victory defence, sending Hooper away.
The former Celtic striker made no mistake, with a cool finish under the goalkeeper, to make amends for his earlier spurned opportunity.
Ball should have extended the Phoenix lead just after halftime, inches away from a Sandoval free kick that flashed across the area.
Substitute Jaushua Sotirio, who replaced Sandoval, had a goal ruled out for a tight but correct offside call, as the Phoenix looked dangerous on the counter-attack.
In the circumstances, Melbourne's 65th-minute equaliser was deflating for the Phoenix. After defending so well, the Phoenix collectively switched off for a moment. Victory skipper Brillante dispatched his shot well but was left free on the edge of the area, after some pinball in the Wellington box.
The Victorian team dominated from there and substitute Nicholas D'Agostino gave them a deserved lead in the 80th minute, after Socceroos veteran Robbie Kruse carved open the Phoenix defence.
Wellington pushed for a miracle but instead conceded late goals to Ben Folami and D'Agostino.
Melbourne Victory 4 (Josh Brillante 65, Nicholas D'Agostino 80, 91, Ben Folami 84)
Wellington Phoenix 1 (Gary Hooper 39).
Halftime: 1-0