The Netherlands, shooting for their third gold in a row, beat New Zealand 4-3 but only netted the winner three minutes from the end after the Kiwis battled back from 3-1 down.
"Not congratulations we won, just phew we won," Dutch forward Ronald Brouwer said, smiling with relief.
The Netherlands are the only team to have won both matches so far, pushing them two points clear at the top of Pool B.
In Pool A, world champions Germany were run ragged by Spain and were lucky to draw 1-1 seven minutes from time.
The Spanish controlled most of the game and didn't give away a single penalty. But they failed to finish off their attacks and when they lined up for corners, they were put off by the German defence running out early and misfired the push-outs.
"The umpires shouldn't have allowed that. These are matches played out in small detail," Spain's coach Maurits Hendriks said.
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Jamie Dwyer, the top scorer so far in Athens, equalised both times and tore up and down the left flank in the last five minutes desperately trying to push in a final winner.
The Indians had more success with a last-minute scoring frenzy that left the crowd and their South African opponents open mouthed.
The eight-times gold medallists have infamously lost their form in the last 20 years but found some of the old running magic as veterans Dhanraj Pillay and Baljeet Singh pulled the team back from an early 2-0 deficit.
With less than two minutes on the clock, India won a penalty corner and then topped it off with a stunning Pillay run and Gagan Singh flick to up their lead to 4-2 with 28 seconds to spare.
Hundreds of Pakistani fans danced with joy as their record-holding penalty shooter Sohail Abbas found his form and netted four goals in their 7-0 win against Egypt.
Earlier, South Korea plucked a much-needed 3-2 victory out of the last minutes of a tough battle with Britain, netting the decider three minutes from time and then defending two British corners won so late that both were taken after the siren.
