The sides remained level for 78 minutes, but the Japan international finally made his mark with a stylish breakthrough goal. This could prove to be a crucial result for the Hoops.
Paulo Bernardo sent a wind-assisted corner sailing directly into the far corner of the net in the first half, but it was disallowed for a foul on Dons goalkeeper Ross Doohan.
Celtic dominated after the break, but some heroic defending and brilliant goalkeeping saw Alistair Johnston and Adam Idah denied. were repelled time and again by heroic Aberdeen defending, led by Slobodan Rubezic.
But a brilliant pass over the top from Greg Taylor found Hatate late on and he fired a shot into the bottom corner to move them seven points clear of their closes challengers with a game in hand.
TrendingThe game was played in heavy rain and wind speeds of close to 50 miles per hour and the quality of football suffered in the first half but both teams had decent chances as the second half progressed.
The Dons had matched Celtic for the first 11 games of the league campaign with both teams' only slip-up coming in a 2-2 draw at Parkhead.
But Jimmy Thelin's side had picked up just two points from three consecutive away games before now losing their 14-match winning run at Pittodrie.
Alex Valle was given some difficult moments by Duk early on and the wide player forced a save off Kasper Schmeichel's legs before Kevin Nisbet dragged the rebound wide.
Duk also had a free-kick saved in a first half of few clear-cut chances. Celtic struggled to get Nicolas Kuhn on the ball and only seriously threatened in the closing stage of the half, through a series of Bernardo corners.
One flew straight into the net but Daizen Maeda was penalised for impeding Doohan on the line with referee Don Robertson deciding the Japan international had backed into the goalkeeper.
Valle had been struggling with a knock and Taylor replaced the on-loan Barcelona left-back at half-time.
Kuhn nearly lit up a scrappy start to the second period but curled just over the top corner following another Bernardo corner.
Duk and Sivert Heltne Nilsen threatened for the home side before the introduction of Luke McCowan and Adam Idah gave Celtic an added edge.
The pair were involved in a move which led to Doohan's first save, an impressive diving stop from Hatate after the Dons defence had made a series of blocks.
McCowan then set up Idah with a curling cross but Doohan made a superb stop from the Irishman's header.
Three of Aberdeen's substitutes were then involved in a move which ended with Leighton Clarkson squandering a good chance from 18 yards.
Taylor drifted inside moments later before picking out Hatate with an exquisite pass and right-back Nicky Devlin played the midfielder onside before watching him slot home.
Ester Sokler had a good chance to level soon after but Auston Trusty managed to divert the substitute's shot over the bar from 10 yards.