Federer, who is playing for the first time in Japan, finally won 4-6 7-5 7-6 after an inspired Suzuki was lifted by his home crowd.
The Japanese player was making his return to the game after a sustaining a serious shoulder injury in January, winning the first set in a memorable comeback performance.
Federer leveled the match at one set apiece, but Suzuki regained his composure to take the last set into a tie-break.
In the end, the Swiss player's class and experience shone through as he easily won the tie-break 7-3 to close out an enthralling match.
Relieved at not being overthrown by a player more than 1,000 places below him, Federer will now play either Finland's Jarkko Nieminen or German Benjamin Becker in the other semi-final.
"I could see the headlines," Federer told reporters.
"'Federer loses to a guy outside the top 1,000.' I'm glad I won - it saved my image."
"His serve is incredible for such a little guy," Federer said.
"I had to dig deep and come up with a good breaker in the end. There's always a fear of losing. It was a relief."
In other quarter final action, South Korean Lee Hyung-taik upset second seed Tommy Robredo 7-6 4-6 6-1 to advance to the semis where he will meet either Tim Henman or Mario Ancic.