Piotr Parzyszek scored for Piast at Borisov Arena in the Belarusian city of Borisov in the 36th minute as the two sides began their European campaign on Wednesday.
Stanislaw Drahun equalised for the Belarusian champions in the 64th minute.
Piast will play BATE in the second leg next Wednesday, July 17, at home.
The winner of the two matches will go on to face either Northern Ireland's Linfield FC or Norway’s Rosenborg BK in the second round of Champions League qualifiers.
The loser will be relegated to the lower Europa League, but will be granted a bye into the second round of qualifiers of the latter.
To qualify for the Champions League group stage, Piast Gliwice need to eliminate the Belarusian champions and three other rivals.
Piast Gliwice in May sensationally won Poland’s top-flight Ekstraklasa football league.
The underdogs, managed by ex-Poland boss Waldemar Fornalik, at the time finished four points ahead of defending champions Legia Warsaw to win their maiden title.
Waldemar Fornalik. Photo: EPA/TATYANA ZENKOVICH
Gliwice is a medium-sized city in Poland’s southern Upper Silesia region.
Source: TVP Sport, PAP, sportowefakty.wp.pl