A steady first half performance saw the hosts on top for large parts, but a dominant second period and another goal for Josh Morris was enough to send all three points back to North Lincolnshire.
United returned to League One action having made three changes to the team that was defeated 3-1 at Charlton last Saturday.
David Mirfin, Neal Bishop and Tom Hopper all returned to the starting line-up at the expense of Charlie Goode, Richie Smallwood and Kevin van Veen.
After a slow opening five minutes, the first half chance fell for the Iron on eight minutes but, after the ball found its way to Josh Morris, that usually reliable left foot fired over.
That chance seemed to kick United into life as, a minute later, a clear-cut opportunity fell to Paddy Madden, but his volley at the far post was well saved by Lee Burge and cleared to safety by the Sky Blues defence.
It took 15 minutes for the home side to forge a first opportunity, when Marvin Sordell crossed to back post and Daniel Agyei was there to draw United into some last ditch blocking.
After the initial scare at one end, United went forward to create an opportunity of their own and, when Morris played in Madden, the former played it across the box but the ball was nipped away from the feet of the lurking Tom Hopper.
Coventry could have taken the lead on 35 minutes when Agyei created his own opening and a clear sight on goal, but he fired well over when he could have been making Luke Daniels work.
Worryingly David Mirfin went down following a challenge after 40 minutes and, after some treatment, it was clear he would be unable to continue, so Charlie Goode came on in his place.
There was time for a late chance for City at the end of the half as Sordell curled one, but Daniels got down well to parry it away for a corner. A foul was then deemed to have been committed by the home side from the resulting corner, and the half time whistle followed not long after.
United started the better of the two sides in the second period and it took just six minutes for a clear-cut opportunity to arise but, sadly for the Iron, Madden couldn’t keep his shot down.
The Iron’s superb start to the second half was richly rewarded on 56 minutes when Madden crossed dangerously and Morris met it to leave Burge with no chance.
Coventry then found their feet after the opener and created a great chance after 71 minutes, but the shot across the box trickled wide.
Then there was an even better opportunity a couple of minutes later, but Conor Townsend put in a superb block from a Jamie Sterry shot to keep the score at 1-0 to the men in green.
Hopper had a golden opportunity to all but seal the win the in 85th minute but, after taking it down on his chest and running in on goal, he stabbed just wide.
There were four minutes’ additional time at the end of the 90, but a solid Iron defensive performance in those four minutes and throughout the second half meant Morris’ goal sealed a tremendous three points at the Ricoh Arena.
Coventry City: Burge (GK), Sterry, Willis (C), Turnbull, Page, Stevenson, Bigirimana, Rose (Reid, 74), Wright (Jones, 64), Sordell, Agyei (Lamerias, 56).
Substitutes not used: Charles-Cook (GK), Harries, Gadzhev, Tudgay.
Scunthorpe United: Daniels, Wiseman, Wallace, Mirfin (Goode, 42), Dawson, Madden (Williams, 84), Hopper, Morris, Bishop, Holmes (Smallwood, 75), Townsend.
Substitutes not used: Anyon, Adelakun, Mantom, Clarke.
Attendance: 9,737 (767 away).