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.
St Mirren continued an excellent week with a 2-1 home victory over Inverness at St Mirren Park.
Danny Lennon's side reached the final of the Scottish Communities League Cup with a 3-2 victory over Celtic on Sunday and Steven Thompson's late header on Wednesday night earned the Buddies their second win in four days.
Esmael Goncalves latched on to Paul McGowan's through-ball to net on his home debut and open the scoring midway through the first half. That was then cancelled out on the stroke of half-time when Billy McKay netted his 20th league goal from the penalty spot after Conor Newton felled Richie Foran inside the box.
Ivan Sproule scored against his old team to earn Ross County a deserved 1-0 victory over Hibernian at the Global Energy Stadium.
A defence-splitting pass from Iain Vigurs found Sproule in space and the winger rounded Ben Williams and stroked the ball into the empty net.
It was County's third win in their last four matches and puts them 14 points ahead of the league's bottom club Dundee, with a game in hand.
St Johnstone capitalised on some hesitant Aberdeen defending as two goals in three second-half minutes moved them above the Dons after a 3-1 win.
Rowan Vine hooked home after a 68th-minute corner and Dave Mackay soon forced home to move Saints into fifth place in the SPL.
Gregory Tade opened the scoring for the home side in the 33rd minute after a mistake from stand-in centre-back Isaac Osbourne but Niall McGinn's superb volley had brought the Dons level a minute before half-time.
John Sutton's late goal broke Dundee's resilience as Hearts bettered their bottom-placed opponents at the third time of asking this season, winning 1-0.
The home side completely dominated the Clydesdale Bank Premier League match but could not force the ball over the line until Sutton's late intervention.
Gary Harkins made his second full debut in a Dundee shirt, playing in the hole behind Colin Nish, but it was the defensive side of Barry Smith's team that deserved the praise after coming so close to recording their third consecutive clean sheet against the Edinburgh side.