"We should have scored well before we did but they could have scored as well, so we rode the storm," Greatholder said.
The Blues made life a little more comfortable for themselves when they struck first in the second half through centre midfielder Tom Biss in the 62nd minute, before teenage striker Kwane Norku pulled one back for the Greeks to 3-1 in the 75th minute. However, the Danny Wilson-captained Blues weren't done, with Stephen Hoyle putting the Greeks out of their misery, 4-1, four minutes later.
Greatholder said: "It was a battle, so we needed to really fight for it, but then our quality came through at the end."
The table-topping Blues are unbeaten after five rounds.
He could not put his finger on the exact time but suspected the Rovers had not beaten Olympic on their turf in almost a decade.
"We wanted to play attractive football but they didn't give us the time to do that."
The Blues host third-placed Wairarapa United, with Paul Ifill as player/coach, at Park Island at 2pm on Sunday.
Greatholder was pleased to have a clean bill of health and having a bye today in the first round of the Chatham Cup (national knockout) competition.
In other games on Saturday, Western Suburbs crushed Palmerston North Marist 8-1, Petone FC and Miramar Rangers drew 1-all, Lower Hutt City pipped Tawa FC 2-1 and Wairarapa United edged Stop Out 3-2 with Ifill among those who found the net.