Suarez volleyed home from Neymar’s cross at the Nou Camp to put FC Barcelona 1-0 up on the night and ahead in the tie on away goals with the scores level at 2-2.
The Uruguayan is the third-fastest player to reach a century of goals for FC Barcelona.
Only Mariano Martin (99 games) and Hungarian striker Laszlo Kubala (103) having taken fewer appearances to reach the landmark.
It took Lionel Messi 188 games to reach 100 goals for Barca.
Neymar put FC Barcelona 3-2 ahead on aggregate after the break when he coolly drilled in a low penalty kick after he was fouled.
But moments later Athletic striker Saborit’s towering header levelled the tie on away goals.
A nervousness engulfed the Nou Camp with the tie heading towards extra-time — until Messi curled in a shot off the post from 20 yards.
The Argentina forward’s strike — his third free-kick in three games in 2017 — put the Catalans into the quarter-finals for the seventh successive season.
The News Agency of Nigeria (NAN) recalls that FC Barcelona have not lost a La Liga game since the start of October.
However, after a series of disappointing draws, FC Barcelona are five points behind arch rivals Real Madrid in the race for the Spanish title.
That means the Copa del Rey may prove to be their best hope of domestic silverware this season.
Club manager Luis Enrique knows what it takes to win this competition, having led the Catalans to success in each of the past two seasons.
It took them to a third triumph in a row, a feat not achieved since 1953.
NAN reports that defeat means Athletic, who are seventh in La Liga, have lost to Barca in the Copa del Rey for the past three seasons.