After spurning a couple of promising opportunities, Kyogo eventually found the net in the 44th minute to give Celtic a slender half time lead.
Rangers attempted to offer a response after the break through Ryan Kent, who saw his effort strike the woodwork.
They were subsequently punished for that miss, though, as Kyogo netted his second of the game to put Celtic on course for the silverware.
Alfredo Morelos managed to halve the deficit in the 64th minute, but Celtic held firm to claim the first domestic trophy of the season.
While the result represents the first defeat of Beale's Rangers tenure, Ange Postecoglu's side are now unbeaten in 24 domestic games.
Against the backdrop of a vociferous Hampden Park, the two famous old foes tussled for control in the opening 20 minutes, which produced little goalmouth action.
The first real shot in anger came from the left boot of Jota, who forced Allan McGregor into a smart save low down to his right.
Rangers' best attacking spell of the first half arrived around the 30th-minute mark when James Taverner's teasing delivery across the face of the goal caused Celtic's Cameron Carter-Vickers to poke the ball behind.
The Scottish Premier League leaders quickly wrested back control, as Kyogo went close on a couple of occasions.
The Japan international curled an effort wide from the edge of the box, while moments later, he guided a header over McGregor's crossbar.
Kyogo refused to be deterred, and his persistence paid off just before halftime when he tapped home from Daizen Maeda's low cross to give Celtic a precious lead.
Rangers attempted to catch their old firm rivals off guard at the start of the second period, with Kent firing an effort against the post, before Fashion Sakala drove the rebound into the side-netting.
They were made to rue that miss as Kyogo doubled Celtic's advantage just six minutes later, bundling the ball into the net from Reo Hatate's squared pass.
Rangers pulled a goal back just after the hour mark when Taverner's dangerous corner-kick reached the back post for Morelos to poke home.
With an equalising goal proving to be elusive, Rangers began to throw caution to the wind, allowing space in behind for Celtic to exploit.
McGregor was required to deny Sead Haksabanovic and Matt O'Riley, before the former fired another effort harmlessly wide.
While a third goal was not forthcoming, Celtic held firm to win the Scottish League Cup for the 21st time in their history.
Sitting nine points clear of the Scottish Premiership table and with a quarter-final to come in the Scottish Cup against Hearts, Celtic will be targeting a domestic treble.