This Europa League encounter was not one which whetted the appetite, but the 21,428 in attendance were treated to a wonderful, entertaining match full of incident.
Kane not only scored his first hat-trick for Spurs but ended the Group C clash in goal after Hugo Lloris' late sending off, although Lamela will take the headlines for his wonderful brace in the 5-1 win.
Many wrote off the man billed as Gareth Bale's heir after a poor, injury-disrupted first season in north London, although this evening he showed a glimpse of the talent that saw Spurs last summer fork out a club-record £30million for his services.
Showing incredible skill and creativity, Lamela wrapped his left foot around his right leg to score with a rabona strike from the edge of the box - a goal any of the greats to don the lilywhite shirt would have been proud of.
Spurs were already a goal ahead at that point thanks to Kane's long-distance strike and their first Group C win was to get better still, with Lamela volleying home from an acute angle before Kane turned home his second from close range.
The 21-year-old wrapped up a hat-trick soon after and then donned the goalkeeper's gloves after Lloris was shown a straight red card for bundling over Tasos Tsokanis
The resulting free-kick from Jeronimo Barrales squirmed through Kane's grasp, but that was not enough to wipe the smile off his face.
The victory was the ideal response to Saturday's 4-1 Premier League loss at Manchester City - a result Pochettino said in his programme notes "certainly didn't reflect what happened".
There were five survivors from the Etihad Stadium defeat in a strong-looking side to face Asteras, including midfielder Etienne Capoue.
The Frenchman has impressed this season but looked sloppy in the early exchanges and was relieved to see a Pablo Mazza strike drift wide after misreading a ball over the top.
It was a rare threatening moment from Asteras, whose goal was breached with just 13 minutes on the clock.
Having already hit wide from distance, Kane tried his luck from 25 yards and his low, fizzing effort went in off the inside of the post.
It was a fine effort reminiscent of the one the England Under-21s international scored against Besiktas - a match in which Lloris' fine display looked set to secure three points before a last-gasp penalty.
The France goalkeeper had nowhere near as many saves to make here, but had to be alert to thwart Facundo Parra, with Ben Davies hacking the follow-up off the line.
Asteras goalkeeper Tomas Kosicky did well to deny Capoue from close range as Spurs looked for a second which arrived in remarkable fashion.
Lamela has struggled to live up to his lofty price tag but showed a glimpse of the magic he is capable of by scoring an incredible rabona kick from the edge of the box.
It was an exquisite strike which took aback those inside White Hart Lane, although head coach Pochettino sat motionless on the bench.
Andros Townsend bent a 20-yard effort just wide before the break, from which the Arkades came out strongly.
Jan Vertonghen blocked a Juan Munafo attempt as the visitors upped the ante, only to go further behind through the man of the moment.
Having produced a full-stretch save to deny Kane shortly before, Kosicky could do little to stop Lamela netting his second as he volleyed home from an acute angle after his initial attempt was blocked.
Lloris had no such problems denying captain Fernando Usero, producing a wonderful one-handed stop to keep out his volley, before Spurs heaped the misery on Asteras.
Kosicky did well to deny Mousa Dembele's shot from the edge of the box finding the net, although the ball fell kindly for Kane to turn home from close range.
The 21-year-old soon ensured he would be taking home the match ball, nodding home a Federico Fazio cross to the back post with nine minutes remaining.
Kane continued in the heart of the action in the closing stages, going in goal after Lloris was sent off for taking down Tsokanis outside the box.
Barrales' free-kick slipped through his grasp but that late consolation could not take the gloss of a special night.
Source : PA
Source: PA