Blues playmaker Tom Biss found the net in the 40th minute from a 30m freekick for the 1-1 equaliser, curling the ball over the wall after hitting the woodwork minutes earlier from another freekick attempt.
Three minutes later, English import Stephen Hoyle unleashed the winner, 2-1, from 40m out with a volleyball, blissfully aware that the goalkeeper was still scrambling back after straying too far out of his comfort zone.
"They threw everything at us in the second half and we looked leggy," said Greatholder, suspecting the 6am start with an early 1.30pm kick-off may have contributed to the lethargy.
The Greeks hit the upright and crossbar but the Blues absorbed the pressure to deny them. Greatholder said Olympic would be a team to watch out for during winter as they would be among front runners.
Player/coach Bill Robertson, defender Fergus Neil and English attacker Saul Halpin cannot play in the Central until their duties are over with Team Wellington in the O-League.
Wellington beat Suva (Fiji) 2-0 on Saturday and, if they make it to the playoffs, the trio will be unable to play the next four rounds for the Blues.
The Rovers, who drew 1-1 with Western Suburbs in the opening round at home, host Wairarapa United at Park Island, Napier, in a 2pm kick-off this Sunday.
Wairarapa beat Lower Hutt City 2-1 on Saturday but lost by the same margin in the opening round away to Stop Out, who thumped Petone 5-1 at the weekend.