The winger let fly with an unstoppable left-foot effort just after the hour in Sunday's quarter-final tie in Malabo to put the icing on the cake for Avram Grant's men, who had already seized control of the contest.
Guinea's spot in the last eight was confirmed via the drawing of lots at the expense of Mali, but their luck ran out as early as the fourth minute when Atsu scored his first from Andre Ayew's superb assist.
Ghana were two goals to the good on the stroke of half-time as Kwesi Appiah showed his predatory instincts to capitalise on a horrendous error from Guinea's Baissama Sankoh for his first international goal.
The second half produced little in terms of goalmouth action aside from Atsu's moment of brilliance and Guinea's misery was compounded in injury time when Naby-Moussa Yattara was sent off for rash challenge on Asamoah Gyan - the goalkeeper having earlier been lucky to escape a red card.
Ghana, who won the last of their four Africa Cup of Nations titles in 1982, can now look forward to a fifth straight semi-final, where hosts Equatorial Guinea await.
Atsu's starring role in the quarter-final tie started in just the fourth minute.
Ayew collected Appiah's pass from the left in the penalty area and the Marseille man showed good strength before his exquisite backheel picked out the run of Atsu, who coolly converted from close range.
With his side struggling for a foothold, Yattara was lucky not to see red as he inexplicably shoved Atsu to the ground.
Aside from the goal, Ghana struggled for clear-cut chances, although Gyan should have done better with a tame shot from the edge of the area.
Guinea proved the architect of their own downfall a minute before the break, though, as Sankoh's bizarre miscued clearance under no pressure fell into the path of Appiah and the Crystal Palace striker clinically side-footed home.
The tempo dropped in the second half with Ghana happy to play possession football, while Guinea appeared shorn of confidence after the first half's late sucker-punch.
Ibrahima Traore wasted a promising set-piece on the hour when he went for goal from a difficult angle with several Guinea players waiting in the area.
Their wastefulness was punished in stunning style just a minute later.
Atsu picked up a short throw-in from the right before cutting inside and unleashing an unstoppable drive over Yattara and into the far corner from an unlikely angle.
Guinea goalkeeper Yatarra's tempestuous game was ended early in stoppage time as he was shown a straight red card for a studs-up challenge on Gyan when one-on-one.
The star striker was left limping by the tackle, potentially giving Grant a headache as Ghana edge ever closer to ending their 33-year wait for glory at the continental showpiece.
Watch every match of the Africa Cup of Nations LIVE on British Eurosport HD or sign up to Eurosport Player and follow the action on mobile, tablet and other devices: www.eurosportplayer.com
