John Savage, 52, beat off the three other contestants after collecting a total of 25 points in the two rounds - specialist and general knowledge.
He recorded 11 out of 14 points for knowing details of Celtic's history, including its founder Brother Walfrid, eminent manager Willy Maley, and a famous victory (over Inter Milan in 1967) and loss (to Raith Rovers).
Elsewhere, he answered correctly on Willie Wallace, Jimmy McGrory, and Henrik Larsson - although he got the last-named mixed up with Shunsuke Nakamura for another question.
His other misses included the name of a stand at Celtic Park which had been demolished during reconstruction, and Celtic's place in the league during a particularly poor season.
Mr Savage, of Polmont, Falkirk, was lying in second place after the first round, but accumulated a further 14 out of 20 in the general knowledge round to win comfortably and seal his place in the semi-finals of the show.
It was the first time that anyone on Mastermind, now hosted by John Humphrys, had picked Celtic as a specialist subject.
The tool salesman earlier revealed he wore Celtic cufflinks during the recording. He added: "Unfortunately I wasn't allowed to wear the Hoops. You're not allowed to wear any football top or anything with a logo on it.
"But I had a pair of Celtic cufflinks and also a replica medal of Lisbon, which I wore on a chain under my shirt, for good luck."
Mr Savage, who is married to Lynne, and is dad to Andrew, 14, lived in Bo'ness for over three decades - where many of his relatives are still based - before moving to Polmont. He works in internal sales at Scott Direct in Grangemouth.