Joe Garner made his first start for the club since his return on a one-month loan last week and fellow new arrival Kallum Higginbotham took a place on the bench as United travelled to the impressive Ricoh Arena for their latest league one fixture.
And it was another very good all-round performance, in front of 951 travelling fans, with goals from Danny Cadamarteri and Danny Livesey which sealed a deserved three points.
"This was a very good performance and I thought we just about deserved the win," manager Greg Abbott said. "We rode our luck at the end a little bit but you would expect a side with this quality to come at us.
"I'd like to say that everybody at this club has been fantastic with us. They've made us feel more than welcome and we really appreciate that. Mark [Robins] has come in and I have no doubt he will turn them around as they have the nucleus of a very good team.
"I have to give credit to our lads because they have defended as a unit and they've created their chances. We've worked hard and controlled long spells so we can take a lot of confidence from it as we go into a massive cup game on Wednesday."
The Cumbrians had the first chance of the day when Murphy glanced a deep free kick from McGovern right at the keeper. Joe Garner followed that up with a wild volley as a half clearance fell at his feet and Coventry struggled to get going as the visitors closed down and scrapped for every loose ball.
The Sky Blues registered their first moment of danger on 14 minutes when McSheffrey arrived late on the edge of the box. He had space but he dragged his right foot shot well wide of the target.
Gillespie was able to claim a looping header from Wood as Coventry committed men forward and determination from McGoldrick created the first clear-cut opening of the day when he beat Livesey to a ball over the top. His low cross whisked across the face of the six-yard box but McSheffrey couldn't quite get there as he slid in to get a touch.
Carlisle regained control as the midfield closed ranks and they earned a penalty from nothing as Garner appeared to be fouled inside the box. Danny Cadamarteri took charge of the spot kick and sent Joe Murphy the wrong way as he stroked the ball into the bottom corner.
Coventry went close to restoring parity with their next attack as Baker broke clear. His shot was touched by a full stretch Mark Gillespie and that took McGoldrick out of the equation. McSheffrey managed to keep the ball in and his eyes lit up as the goal opened up in front of him. It was a tight angle and he wheeled away in disappointment as he smashed his effort into the side netting.
It was a short-lived reprieve for Carlisle though as a shot from Fleck grazed Murphy's head and went over the bar for a corner. The set piece was cleared but Baker lobbed it back into the area as United tried to regroup. McGoldrick held his ground and picked his spot with a neatly placed nod down.
United responded well with some good possession play and a cross from Cadamarteri cannoned into Garner. He stumbled at the near post and Joe Murphy ignored his attempt at a back heel as he gratefully dropped on top of the loose ball.
Baker was in the thick of the action again just after the break when he twisted and turned his way into the area. He had options left and right but he went for a shot which Gillespie pushed behind.
McGovern brought the save of the day out of Murphy as Carlisle got forward with intent when Garner cushioned a Cadamarteri cross into his path. His volley was crisp and needed a two-handed parry to stop it from going in.
McGovern turned provider from the resulting corner and Danny Livesey muscled his way through a gaggle of bodies to make the cross his own. He was able to punch the air in celebration as his header whistled into the top corner.
Carlisle looked good for their lead and a cross from Robson was just an inch in front of McGovern as he threw himself at getting a touch.
Coventry made changes and threw caution to the wind as they went in search of an equaliser, and a shot from Fleck spun just wide as it deflected off Peter Murphy and wrong-footed Gillespie.
And McGoldrick smashed an instinctive effort off the upright as he tried to find the finish to unlock the increasingly stubborn defence.
Substitute Cody McDonald was next to hit the woodwork as he found a yard to prod the ball past Gillespie. Chantler hooked it clear as it bounced around dangerously inside the box.
"I don't think we were as good with the ball as we could have been, but we defended well as a team," Livesey said. "It's always nice to score and it's been a while since I got a winner. It was a great ball from JP [McGovern] and it was just a case of me gambling and getting in there. It's set us up nicely for the game against Tottenham now."
Coventry - McGoldrick (38)
United - Cadamarteri (25 pen), Livesey (57)
Coventry - Clarke (18), Baker (60)
United - Thirlwell (79)
Coventry City - Murphy, Clarke, Baker, Fleck, McSheffrey (McDonald 70), Jennings (Henderson 23), Kilbane, Wood, Daniels (Reckord 65), McGoldrick, Brown. Subs - Dunn, Elliott, Edjenguele, Willis.
Carlisle United - Gillespie, Simek, Livesey (Edwards 89), Murphy, Chantler, McGovern, Thirlwell (Potts 82), Berrett, Robson, Cadamarteri, Garner (Higginbotham 84). Subs - Collin, Noble, Beck, Symington.
Referee - Mr Patrick Miller
Attendance - 10,674 (951 away fans)