Lotto Central League reputations meant nothing after hosts Wellington Olympic came close to doing the unthinkable with 10 men against the league leaders after losing captain Mikey Halikias to a straight red card in the 17th minute for a crude tackle on striker Angus Kilkolly.
But it was Haidakis who drew first blood two minutes before halftime with his long-range missile that caught Rovers keeper Ruben Parker Hanks napping.
"We had a lot of possession and opportunities to be 2 or 3 goals up into halftime but our execution was not there," Robertson said of the Danny Wilson-skippered side.
It wasn't until eight minutes into the second half that Kilkolly equalised, 1-1, from a penalty kick after winger Harry Morton was hacked down in the box.
That sustained pressure yielded another penalty kick in the 68th minute when this time striker Saul Halpin was "taken out". League golden boot contender Kilkolly stepped up again to put the visitors ahead 2-1.
Declared Robertson: "Both of them were clear-cut penalties."
However, Haidakis, who found the net in the 79th and 81st minutes with almost identical headers from cornerkicks to put the Greeks up 3-2, begged to differ.
"The first one was a penalty but the second one wasn't because there was a foul before that and the referee didn't see it," he said.
Rovers defender Finlay Milne grabbed the 3-3 equaliser in three minutes of regulation added time to push the game into 30 minutes of extra time after nodding in a header from a cornerkick.
American university scholarship student Morton was the toast of the Blues just two minutes into extra time after tapping home a Halpin cross from the back post to seal the 4-3 victory.
Milne left the field in the second spell of extra time after collecting his second successive yellow card but the Rovers hung on for victory.
"We expected a very tough game. We didn't defend well and conceded sloppy goals but showed character in the end," Robertson said, keeping his fingers crossed for a home quarterfinal when names are drawn out from the hat today after two matches on the road.
Haidakis, lauding his team for soldiering on with 10 men, was scathing of the whistle blower and questioned the equalising corner in added time.
"The ref got a little too involved and handed them two goals so we can't do much about it now," he lamented, happy with his hattrick but emphasising he also valued the mantle of provider for Olympic who travel to Park Island for a 2pm league kick off this Sunday.
Eastern Suburbs beat Tauranga City 5-3 on penalties after they were tied 1-1. Birkenhead Utd edged out East Coast Bays 2-0, Central Utd beat Three Kings 2-0, Mangere Utd prevailed 3-1 over Papakura City, Western Suburbs bullied Wairarapa 7-2, Cashmere Tech overwhelmed Coastal Spirit 3-1 and Dunedin Tech flogged Mosgiel 6-1.