In the second minute of stoppage time, with the score 1-0 to Reggina, Inter looked to be heading out of the competition on the away goals rule.
But Argentine striker Julio Cruz's long-range drive struck the post, bounced off Belardi's head and rolled into the net to give the visitors an unlikely 1-1 draw on the night and a 3-2 aggregate win.
Reggina midfielder Julio Leon put his team ahead in the 38th minute when he nodded in Gianluca Falsini's cross at the far post.
The home side were then reduced to 10 men after defender Simone Giacchetta committed a second bookable offence, but Inter failed to take advantage of their numerical superiority.
Reggina defended well and nearly made it 2-0 shortly after the interval when striker David Di Michele headed narrowly over the bar, before Inter's late goal provided an agonising finale to the home side's evening.
Inter's quarter-final opponents will be the winner of Thursday's fixture between Bologna and Udinese.
In an earlier match AS Roma moved through to the quarter-finals with a laboured 2-1
The victory gave the Serie A leaders a 3-1 aggregate success in the second round tie.
DELVECCHIO STRIKE
Inspired by playmaker Eugenio Corini, Palermo dominated Roma early on and took the lead in the 30th minute when striker Simone Pepe headed Corini's cross past Roma reserve keeper Andrea Zotti.
Shorn of several first team regulars including Francesco Totti, Roma lacked ideas and were fortunate to equalise in the 69th minute when a Damiano Tommasi lob took a deflection and ended in the back of the net.
Eleven minutes later striker Marco Delvecchio made it 2-1 when he shook off his marker to slot home a low cross from close range.
In the last eight Roma will face the winner of Thursday's fixture between AC Milan and Sampdoria, which European champions Milan lead 1-0 after the first leg.
Lazio and Parma set up a quarter-final clash by beating Modena and Venezia respectively on aggregate. Parma lost 1-0 at home to Serie B team Venezia but went through 2-1 overall.
