Th 24-year-old has now scored in each of Union's three Bundesliga games and forged a partnership alongside Germany striker Max Kruse.
Awoniyi's transfer from Merseyside was made permanent this summer after spending last season on spell at Union, where he managed a total of five goals.
Winger Niko Giesselmann gave Union an early lead, then a great through ball from Kruse put Awoniyi into space in the area.
The Nigerian rounded Gladbach's Swiss goalkeeper Yann Sommer and tucked his shot into the net from a tight angle just before the break.
Awoniyi proved he can create chances as well as finish them in the second half when his pass put Levin Oztunali in space but the central midfielder fired just wide.
The visitors scored a late consolation goal when Jonas Hofmann tapped the rebound in the net after a shot by substitute Laszlo Benes was saved.
Union are eighth after their first win in three league games.
Gladbach are down near the foot of the fledgling table with a point after a draw with Bayern Munich on the opening day of the season before defeats to Leverkusen and now Union.
Standout matches today