Rangers scored two late goals last week to take a slender lead into Thursday's reverse fixture and extended their lead inside nine minutes through Alfredo Morelos' strike en route to a 9-5 aggregate victory.
Lior Refaelov added to his goal and two assists from the first leg by equalising for Antwerp in Glasgow, but substitute Patterson - given a reprieve by Gerrard after his recent breach of coronavirus protocols - made an instant impact to put the Gers back in front.
Ryan Kent gave the host more breathing space nine minutes later and although Didier Lamkel Ze pulled one back another for Antwerp, Borna Barisic and Cedric Itten netted late penalties as Rangers reached the last 16 for the second year running.
Kent was among the scorers in the gripping first leg and was involved from the off here, testing Ortwin De Wolf with a low drive before picking Jeremy Gelin’s pocket and setting up Morelos for a simple finish.
Rangers had won just one of their four Europa League knockout matches at Ibrox and they were pegged back by Refaelov's deft finish following some good play out wide from Jordan Lukaku.
Gerrard replaced Leon Balogun with Patterson at the interval and that paid instant dividends as the teenage right-back, a surprise inclusion in the matchday squad, got in behind and picked out the bottom corner 16 seconds after being brought on.
Morelos then repaid the favour to Kent for the earlier assist by knocking the ball past Martin Hongla and crossing for his team-mate to finish, giving Rangers a three-goal advantage on aggregate.
Antwerp, competing in their first major European knockout match since 1994-95, gave themselves hope thanks to Lamkel Ze's tap-in following a comical coming together between Connor Goldson and Allan McGregor.
But Rangers extended their lead through Barisic's penalty - awarded for Maxime Le Marchand's trip on Morelos - which was followed up by another from the spot in the closing stages, converted by Itten.