Wilfried Bony's second-half equalizer looked set to send the Africans into the knockout phase but the striker's spot kick in the dying seconds booked a clash with Costa Rica.
Georgios Samaras' last-gasp penalty saw Greece beat Ivory Coast 2-1 and reach the FIFA World Cup's last 16 for the first time.
Needing a win to qualify in Fortaleza on Tuesday, Greece left it late, with Samaras' 93rd-minute spot kick sealing the team's progression in dramatic circumstances.
The penalty was given after the forward was tripped by Giovanni Sio and the Celtic man dusted himself down before scoring to Boubacar Barry's left.
A draw would have been enough for Ivory Coast to progress and that looked likely when Wilfried Bony came off the bench to level proceedings with 16 minutes left.
Greece had initially taken the lead through Andreas Samaris – an early replacement for the injured Panagiotis Kone – in the 42nd minute.
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The Europeans had also hit the bar earlier, through Jose Holebas, and the woodwork was to deny them again in the second half as Giorgos Karagounis saw his 35-yard strike bounce away to safety.
But Greece claimed a deserved win as Samaras kept his nerve, setting up a clash with Costa Rica in the round of 16.
Yaya and Kolo Toure both started, after deciding to stay in Brazil following the death of their brother, while captain Didier Drogba made his first start of the tournament, replacing Bony.
Greece's start was thrown into disarray by two forced substitutions inside the first 30 minutes, as Kone and goalkeeper Orestis Karnezis suffered injuries.
But the Greeks almost took the lead in the 33rd minute from a quick break, as Holebas – played in following Samaras' well-weighted through ball – saw his fierce strike come back off the crossbar.
The goal frame did not come to the rescue of Barry nine minutes later, though.
A stray pass from Cheick Tiote saw Samaris pounce, and he combined well with Samaras before coolly slotting past the goalkeeper.
Ivory Coast continued to control possession, but failed to convert it into regular chances.
Greece's threat on the counter only grew as the second half progressed and Ivory Coast was rescued by the bar for a second time with 22 minutes to go, when captain Karagounis tried his luck from 35 yards.
The introduction of Bony gave Ivory Coast another dimension and after wasting a pair of half chances, the Swansea City forward drew his side level, producing a composed first-time finish after Gervinho's clever cut back.
But it was the Greeks who looked more likely to score the winner, as Dimitrios Salpingidis flashed an effort wide, before Sio's foul gave Samaras the chance to be a hero.
It was an opportunity he took with both hands, slotting past Barry to earn Fernando Santos' side a place in the next round.