Andros Townsend's first-half penalty and a Harry Kane header minutes later proved the difference at the Theodoros Kolokotronis Stadium as Spurs secured back-to-back Group C wins.
It was nowhere near as straightforward as it should have been, though, with Asteras deserving much more than Jeronimo Barrales' late consolation goal and a 2-1 home defeat.
Few could have predicted such a flaky Spurs display after a dominant, if uninspiring, opening period in which Townsend opened the scoring from the spot.
The England winger provided a fine cross shortly afterwards for Kane to net his eighth in as many games, making a scoreline similar to the 5-1 thumping in the reverse fixture two weeks ago look possible.
However Asteras, playing in what manager Staikos Vergetis called the biggest match in their history, dominated the second half from the outset, with Tasos Tsokanis coming close seconds after the restart.
That effort was reminiscent of Sammy Ameobi's game-changing goal for Newcastle at White Hart Lane last month and, yet again, Spurs failed to adequately respond.
Asteras attacked with renewed vigour and Facundo Parra twice wriggled free only to miss gilt-edged chances, before Pablo Mazza crashed a strike off the post.
The central defensive pairing of Jan Vertonghen and Federico Fazio looked rattled, with the latter receiving the second red card of his short Spurs career in stoppage time
Barrales scored the resulting penalty but Asteras could not quite squeeze a leveller, as Spurs rode their luck.
Source : PA
Source: PA