John McGinn opened the scoring for the visitors before the break to extend their aggregate lead to 4-2 before Tripolis responded through Kosmas Tsilianidis even though the home side had Michael Manias sent off for two bookings moments earlier.
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Despite Hibs’ numerical superiority, it was Savvas Pantelidis’ side who finished the second leg on the ascendency, squandering several notable chances against an excellent Adam Bogdan.
French referee Benoit Millot’s final whistle was warmly greeted by the Hibs players and around 1,500 travelling supporters as Neil Lennon’s side set up a third qualifying round clash with Norwegian side Molde.
UEFA, however, are likely to take a dim view of the flares, including one thrown on to the pitch following McGinn’s strike and smoke bombs that were set off by the Hibs fans.
The significant pre-match team news for the visitors was that influential striker Flo Kamberi was deemed fit to start despite sitting out the previous evening’s training session due to a knee complaint.
The Swiss, whose right leg was heavily strapped, lined up alongside Martin Boyle in attack as Lennon made one change, David Gray replacing Steven Whittaker, from the team that produced a stirring comeback to win the first leg 3-2.
Despite an afternoon deluge of rain hampering the vocal travelling support’s alfresco drinking in the Peloponnese capital, the pitch was in perfect condition on a balmy night under the floodlights.
In a ground named after venerated Greek general Theodoros Kolokotronis, who oversaw the bloody war of independence against the Ottoman Empire between 1821 and 1829, Hibs began the match determined to hold their ground behind enemy lines.
A slow start to the game suited Hibs as they settled into the unfamiliar surroundings but captain Gray was twice called upon in quick succession from the seventh minute to make timely interceptions.
The right wing-back did well to clear a menacing cross from Ioannis Kotsiras before the 2016 Scottish Cup winning hero took the ball off the feet of Manias as the striker was about to shoot from inside the box.
The Leith side were struggling to retain the ball for any sustained period during the early jostling, although fashioned the first meaningful opening in the 14th minute.
Vykintas Slivka’s deft pass found the unmarked Boyle just six yards out but a poor first touch allowed Jose Luis Valiente to recover and make the block on the shot.
Hibs kept up the pressure from the corner and Boyle then had a low drive from the corner of the box saved by Giorgos Athanasiadis at the goalkeeper’s near post.
Watching on from the modest main stand, Hibs manager Lennon, who was serving a final UEFA ban, would have been relatively content by his side’s start.
Indeed, the Easter Road side registered another shot on target in the 19th minute, albeit Stevie Mallan’s ambitious free-kick from 30 yards was comfortably held by Athanasiadis.
A dramatic ending to the half saw Hibs draw first blood after riding their luck at the other end.
Defender Paul Hanlon prevented what would have been easy tap in for Nikos Kaltsas at the back post with a crucial headed clearance in the 40th minute before Kosmas Tsilianidis glanced a header off the bar from Giorgos Kiriakopoulos’ corner.
The visitors then stormed ahead two minutes before the interval when Kamberi dispossessed the dithering Mathias Iglesias before setting McGinn free, and the Celtic-target forced a shot across the goalkeeper into the net to spark joyous scenes in the stand behind the goal.
An encouraging performance got even better for Hibs three minutes after the restart when Manias, just moments after having a shot blocked by goalkeeper Bogdan, collected a second booking for a late challenge on Hanlon.
However, the hosts breathed fresh life into the tie by levelling on the night in the 56th minute.
Tsilianidis turned Efe Ambrose outside the area and struck a low left-footed drive beyond Bogdan from 18 yards.
Hibs were rattled as Asteras went about turning the tie in their favour. Bogdan palmed a rising drive from Ioannis Kotsiras over the bar before getting down so substitute Taso Douvikas’ header.
Iglesias then headed wide from close range before frantic appeals for a penalty were waved away after Douvikas went down under a challenge from Bogdan.
The Hibs keeper was his team’s saviour again in the 83rd minute with another save to deny Kotsiras.
But Hibs were able to see the game out to cap another memorable European night.
Asteras Tripolis: Athanasiadis, Kotsiras, Triantafyllopoulos, Valiente (Salas 90), Kiriakopoulos, Iglesias, Bellocq (Douvikas 57), Kaltsas (Rolle 78), Munafo, Tsilianidis, Manias. Subs not used: Papadopoulos, Christopoulos, Martinez, Bastianos.
Hibs: Bogdan, Ambrose, McGregor (Whittaker 78), Hanlon, Gray, Slivka (Bartley 89), Mallan (Porteous 90), McGinn, Stevenson, Boyle, Kamberi. Subs not used: Laidlaw, Swanson, Martin, Shaw.
Referee: Benoît Millot (FRA)