Red Star Belgrade, meanwhile, deadlocked 0-0 with visiting Salzburg in the Tuesday's other match, reports Efe news.
PSV, who won Europe's elite club competition 30 years ago, fell behind early in Borisov, conceding a goal to Jasse Tuominen in the 9th minute, but pulled level in the 35th minute as Gaston Pereira converted from the penalty spot.
The visitors took a 2-1 lead just after the hour mark on a strike by Hirving Lozano and seemed assured of victory until the 88th minute, when veteran Alexander Hleb equalized for BATE, a minute before PSV's Donyell Malen scored to nail down the win.
Benfica, trying to get back to the Champions League after an absence of eight years, created a ton of chances against PAOK, yet their only success came from the penalty spot: a conversion by Pizzi Fernandes in first half stoppage time.
The Greek side, who eliminated the likes of Basel and Spartak Moscow to reach the final qualifying round, are in pursuit of their first experience of Champions League football.
With less than 15 minutes left in regulation, PAOK's Amr Warda pounced on the rebound after a shot by teammate Fernando Varela hit the cross-bar and put the ball in the net to make it 1-1.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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