Basel's hopes of getting any result and piling pressure on Liverpool in their quest to reach round two were dashed when Serey Die was sent off 18 minutes in for a challenge on Cosmin Moti. Replays suggested that the midfielder was unlucky to be dismissed.
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However, they tried to forge an unlikely lead midway through the opening period when a speculative effort from Derlis Gonzalez almost nestled in the top corner of the Ludogorets net, but for the intervention of Vladislav Stoyanov.
Ludogorets' one-man advantage appeared to show in the balance of play as Fabio Espinho found himself on the end of two chances in as many second-half minutes, but could take neither.
The Portuguese midfielder then had another opportunity midway through the half. However, his shot was blocked by a resilient Basel defence who could perhaps scent an unlikely point.
With 11 minutes remaining, Mihail Aleksandrov rose highest to meet Minev's cross, but his header was agonisingly wide as Ludogorets desperately searched for a late winner.
Minev then popped up in injury time with a strike that appeared to take a deflection before beating a helpless Vaclik and giving the Bulgarian side victory.