Hatate put Celtic ahead after 14 minutes before Furuhashi got in on the act, doubling the Hoops’ lead soon after and then grabbing his second just before the break when he tapped home from James Forrest’s square ball.
Celtic went four up shortly after half-time when makeshift right-back Hatate slotted into the far corner following a VAR check but St Johnstone pulled a goal back courtesy of Drey Wright’s rebound effort.
The win saw Celtic once again move nine points clear of second-placed Rangers, who beat Ross County 1-0 on Friday night thanks to John Lundstram’s first-half effort.
Also on Saturday, St Mirren came from behind to pick up their first win in five with a 3-1 victory over 10-man Aberdeen – despite the hosts missing two of their three penalties.
O’Hara made no mistake from the spot a second time as he gave his side a 53rd-minute lead but Jonah Ayunga spurned the chance to extend their advantage when he too failed to convert a penalty.
United regained their advantage through Dylan Levitt two minutes after half-time and thought they had all three points but, deep into stoppage time, Ross Graham brought Shankland down inside the area, and he picked himself up to dispatch the penalty and share the points.
Magennis added his second of the match five minutes after the break to end their losing streak in style, with Livi’s misery completed when they missed two late penalties through Esmael Goncalves and Jack Fitzwater.