The 28-year-old opened the scoring with a close range tap-in on the stroke of half time, before adding a second with a similar finish inside the six-yard box on the 56-minute mark, sending the Hoops supporters behind the goal into pandemonium.
Alfredo Morelos pulled one back for Rangers eight minutes later, but Celtic held firm to continue their dominance in the League Cup, retaining their title and lifting the trophy for the seventh time in the last nine seasons.
Furuhashi proved to be Celtic's Hampden Park hero for a second successive year, after also scoring a double in last season's League Cup final win over Hibernian.
In doing so, the Japan international has become just the second Celtic player in history to score back-to-back braces in League Cup finals after McPhail, who scored successive doubles back in 1956 and 1957 - netting a hat-trick in the latter year.
Furuhashi, who has established himself as a star player under Ange Postecoglou since joining the club in July 2021, has now taken his impressive goal tally to 24 in 35 appearances across all competitions so far this season.
Meanwhile, Celtic captain Callum McGregor has now won 17 major trophies with Celtic - including six League Cups - and is still yet to lose a cup final in his professional career with the Hoops.
The 29-year-old has also won all 13 finals that he has played in for Celtic at Hampden Park, winning five League Cups, four Scottish Cup and four Youth Cups.
McGregor hailed the atmosphere the Celtic fans created in Glasgow and labelled teammate Furuhashi a "special player" following his man-of-the-match display in the final.
"[Furuhashi is] a special player," the midfielder told BBC Sportsound. "[Winning another final] means the world to me. Time after time, you're tasked to win at this club.
"This is a special group. We can do both sides of the game. Listen to this place. It's rocking."
Postecoglou was also full of praise for Furuhashi after the match, adding: "Sometimes the measure of a footballer at this club is whether you can deliver on the big occasions.
"He's just an unbelievable young man in terms of his personality. He's such a clever player and he wants the big moments. He delivered again."
"Moments like this, you want to get the whole experience," Postecoglou continued. "You watch the players, the fans, what it means to them. I take great pride in it."
Celtic's hopes of winning a domestic treble remain alive, and as soon as their deserved celebrations settle down, their focus will shift back to the Premiership with a trip to St Mirren up next on Sunday.