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, who got the response he wanted after his side were knocked out of the Scottish Communities League Cup by St Mirren at Hampden on Sunday, was the injuries picked up by Izaguirre and Georgios Samaras.
He will hope both will have recovered for next month's Champions League last-16 clash with Juventus.
Killie will feel they were denied the opening goal but Kenny Shiels' side, which included teenagers Barbour, Mark O'Hara, Jude Winchester and Rory McKeown and 20-year-old William Gros, in the starting line-up were well beaten in the end.
In an encouraging start by the hosts, Commons grazed the bar with a 25-yard free-kick in the ninth minute, his effort taking a deflection on the way over to win Celtic a corner which Killie defended.
Five minutes later, Samaras was sent through by Commons but the Greece striker let the ball run away from him and ended up hitting the side-netting as Killie keeper Cammy Bell raced out to block.
As Lennon's side stepped up a gear, Commons sent a drive from the edge of the box crashing against the bar before Bell had to stretch to save a low drive from Gary Hooper, the corner again proving fruitless for the hosts.
The next chance for Celtic came soon afterwards when Izaguirre whipped in a great cross from the left but most of Celtic Park groaned as Charlie Mulgrew headed over from barely six yards out.
The Honduran then went off after appearing to pick up a leg injury to be replaced by Ledley.
Seconds later, Barbour, under pressure from Mulgrew at the back post, appeared to help force the ball just over the line from McKeown's cross only to be left fuming when referee Murray failed to award a goal, presumably taking his cue from the linesman who kept his flag by his side.
Bell was soon to be tested again when he had to parry Hooper's drive and Killie's Mo Sissoko defended brilliantly in taking the ball off the toes of Samaras who was ready to knock the ball in.
However, that only delayed the breakthrough for the home side which came in impressive style when Ledley drilled in a 30-yard shot which gave the flailing Bell no chance.
A minute before the break there was more worry 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.
Sheridan drew Killie level in the 47th minute when he slotted in a cross from William, only for Matthews to restore the home side's lead three minutes later with a powerful right-footed drive from 25 yards.
Celtic went looking for number three and in the 61st minute, after Lukasz Zaluska had made a good save from Barbour at the other end, Commons over-elaborated when he was set up by Hooper and his chip from eight yards went wide of the target.
Commons then had a drive save at the second attempt by Bell before Hooper missed a sitter after Matthews had set him up six yards out with a great cross from the right.
In the 72nd minute the strangely listless Hooper again missed a good chance after being set up by Watt, the Norwich target dithering long enough to allow Bell to foil.
In the 76th minute Killie defender Jeroen Tesselaar burst into the Celtic box, taking the home side by surprise but volleyed just over the bar and was soon made to pay for passing up what was a good chance.
Celtic ran down the other end and, when Hooper set up Stokes, he 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.