Basel held off a spirited Frankfurt to book a Europa League quarter-final against Shakhtar Donetsk.
The Swiss side held a three-goal advantage from the first leg in March, played before the coronavirus shutdown.
Frankfurt started brightly in search of an early lifeline and centre back Martin Hinteregger went close with a header.
The visitors enjoyed plenty of possession but they could not find a way past Basel goalkeeper Djordje Nikolic.
Basel midfielder Valentin Stocker went close with a fine run and chip over the advancing keeper but Kostic cleared off the line.
Fabian Frei finally broke the deadlock in the 88th minute.