Killie teenager Ross Barbour thought he had squeezed the ball over the line in the 37th minute only for referee Calum Murray to wave play on, and the visitors' frustration was compounded three minutes from the interval when Hoops substitute Joe Ledley - on for Emilio Izaguirre - fired the hosts into the lead with a long-range drive.
Former Celt Cillian Sheridan levelled two minutes after the break before Matthews arrowed in a shot from 25 yards and, after Anthony Stokes - on for Kris Commons - grabbed a third, the Wales international sealed a convincing win from close range to take the champions 15 points clear of Inverness at the summit.
The only real downside for manager Neil Lennon was injuries picked up by Izaguirre and Georgios Samaras.
The home side went ahead in the 41st minute when Ledley drilled in a 30-yard shot which gave flailing Kilmarnock goalkeeper Cammy Bell no chance.
But a minute before the break there was concern for Lennon when Samaras had to be replaced by Tony Watt after going down with what looked like a hamstring injury.
The second half began with a bang as Sheridan drew Killie level in the 47th minute when he slotted in a cross from William Gros, only for Matthews to restore the home side's lead three minutes later with a powerful right-footed drive from 25 yards.
Celtic scored a third on 78 minutes when Gary Hooper set up Stokes, who calmly rounded Bell before sliding the ball into the net for his first goal of the season as he continues on his recovery from an ankle injury.
Stokes then turned provider when he crossed for Matthews to knock in from a yard out with seven minutes remaining and, with Killie limping to the end, there was still time for Hooper to crash a shot off the post.