Stand-in skipper Joe Ledley scored twice as Celtic cruised to a 5-0 win over SPL bottom club Dundee at Celtic Park.
Ledley scored once in each half, while James Forrest and Dylan McGeouch were also on target and Gary Hooper netted for the first time in six matches as the hosts extended their lead at the top of the table to 21 points.
The Dark Blues thought they had taken the lead after just five minutes when Gary Harkins' free-kick crept in at the near past but an alert linesman spotted that John Baird had strayed offside.
Neil Lennon's side soon reasserted their control and were ahead through Ledley, who captained the team in the absence of the injured Scott Brown.
Dundee keeper Rab Douglas could only palm an Emilio Izaguirre cross into the path of Ledley and he slotted home from eight yards (13).
Gary Irvine then pulled off a crucial block to deny Forrest's goalbound effort before Hooper came to the fore.
First he fired over following some neat link-up play with strike partner Anthony Stokes before Douglas palmed away a stinging effort, with a subsequent low angled drive fizzing just past the upright.
The visitors briefly rallied, with Fraser Forster doing well to tip a deflected Harkins shot over the bar.
The same player was then denied soon afterwards, his header bouncing up off the turf before hitting the crossbar.
That was as good as it got for the Taysiders though as they were reduced to 10-men early in the second half and conceded from the penalty spot.
Matt Lockwood, only on the pitch for three minutes after coming on as a half-time substitute, was dismissed on 48 for bringing down Hooper right in front of goal and Forrest send Douglas the wrong way with his spot-kick.
Stokes then scuffed an inviting shot past the post but Dylan McGeouch killed the game off with a header into the top corner after the impressive Stokes had clipped the ball into the box (57).
Ledley notched up his second goal of the contest when he curled left-footed into the top of the net after Stokes had laid the ball off to him, with Dundee struggling to cope (73).
Celtic continued to press and Hooper ended his mini goal drought in emphatic fashion seven minutes from time, controlling Ledley's ball into the box before volleying home.
Boyd, who scored 164 goals across spells with Killie and Rangers between 2001 and 2010, re-signed before Saturday's 1-1 draw with Aberdeen at Rugby Park in the SPL.
"It was great to get him in and it's great to have that type of person back in the squad," said Shiels. "He will be back in with us on Monday and we will work from there. It's self-explanatory what he will bring to us - he is the top scorer of all time in the SPL (era).
"There's a hunger there and I can see that, I think he's an excellent professional who has served the game well and we are excited about that."
Kilmarnock were fortunate to claim a share of the spoils against the Dons. Rory Fallon's brilliant volley gave Aberdeen the lead they deserved before Paul Heffernan got Kilmarnock back on terms five minutes before half-time.
Aberdeen passed up a number of good chances to grab a vital second goal and were denied a penalty with 15 minutes remaining when Kilmarnock goalkeeper Cammy Bell appeared to foul Niall McGinn in the penalty area.
Shiels would not be drawn on the controversial decision, saying: "I'm trying very hard to discipline myself not to speak about referees.
"I'm not allowed to speak about referees and I'm not allowed to speak about other teams because they'll fall out with me."
Aberdeen striker McGinn was baffled after receiving a yellow card for diving in the incident.
"In my own eyes and in the eyes of a few of the Kilmarnock players too it was a stonewall penalty - I think the referee was the only person inside the ground that didn't think it was a penalty," said McGinn.
"I was chasing the goalkeeper down and he took a bad touch, I thought I was going to raid him then he brought me down.
"You just have to get on with things, being a professional footballer you just have to get on with things."
The Dons now face a crucial encounter against Ross County on Tuesday evening and the Northern Ireland international believes they can take confidence from their display at Rugby Park.
"We played well against Kilmarnock and we have to take that into our game against Ross County," he said.
"Hopefully on Tuesday we can take our chances."
