Reo Hatate scored his first goal for six months to kick-start Celtic’s 3-0 win over St Mirren. Hatate produced a classy finish as Celtic recovered from a slack and goalless first half to take ­control of the game early in the ­second period. Hatate has endured an injury-hit 12 months but he stepped up his ­comeback from calf problems by ­easing the tension around Celtic Park. Kyogo Furuhashi and Adam Idah also ­scored as the Premiership leaders moved four points ahead of Rangers, who have still to play twice before the split. With Daizen Maeda absent with a hamstring problem, Celtic missed the wide player’s dynamism in a tepid first-half display. The visitors looked the more threatening team in the opening half. Greg Kiltie had a great opportunity from Toyosi Olusanya’s square ball but could not make the required contact. Ryan Strain had an effort blocked and Olusanya fired over. Whatever Brendan Rodgers said at half-time had the desired effect as Celtic immediately stepped up ­several gears. Furuhashi glanced a header wide when Cameron Carter-Vickers looked likely to score behind him but Celtic did not have long to wait for the breakthrough in the 52nd minute. Alistair Johnston’s pass inside found Hatate and the Japan midfielder took a touch before quickly guiding the ball into the top corner with the ­outside of his boot from 16 yards. Yang Hyun-jun miskicked when presented with a good chance moments later but Furuhashi doubled the lead on the hour mark when he headed home Johnston’s cross from six yards. Zach Hemming saved from Greg Taylor, Hatate and substitute Luis Palma as Celtic kept up the pressure. St Mirren lost Scott Tanser and Kiltie through injury at the start of the second half and the ­visitors were now struggling to impose themselves. Callum McGregor was among four Celtic ­substitutes who came on in the 71st minute and the home side were able to make a sixth replacement, James Forrest, because of Elvis Bwomono’s concussion. The winger came close before being involved in the move that led to Idah nodding home from close range in the 86th minute as Celtic ­outnumbered the visiting defence. Rodgers insisted he said “­nothing overboard” at the break as his side overpowered St Mirren in the second half. “I just felt that in the first half we were a bit passive in our pressing and counter pressing,” Rodgers told BBC Scotland. “We didn’t keep the ball well enough to combine and sustain the attack. It was just about maintaining the patience and speed of the game and, once we get the goal early in the second half – great combinations and finish from Reo – these types of games, when the opposition is tight and compact, the first goal is critical. “The players were outstanding for the remainder. It is a huge credit to the players. Everything started to connect much better and cleaner.”