Brighton loanee Leo Ostigard headed home the winner for his second goal in three games
Coventry City climbed six points clear of the Championship relegation zone with a vital win at fellow strugglers Rotherham.
Millers goalkeeper Viktor Johansson made superb saves to deny Liam Kelly and Tyler Walker, while home midfielder Lewis Wing smashed a shot against the post in an entertaining first half.
The Sky Blues took the lead when Leo Ostigard powered in a header that took a deflection on its way past Johansson.
Rotherham, who were playing their second game in 48 hours, could not really create anything in response and they are now four points behind 21st-placed Derby.
They have two games in hand on the Rams and that will be three by the time they host Birmingham on Sunday in what will be their fourth game in nine days.
However, boss Paul Warne will need to pick his players up after a night where they were second best for much of the game and failed to force visiting goalkeeper Ben Wilson into a save.
- Relive Coventry's victory at Rotherham as it happened
Norwegian defender Ostigard won it in the 70th minute when he met Matty James's chipped free-kick into the area and his downward header beat Johansson after taking a slight nick off Millers defender Wes Harding.
In truth Coventry, who picked up just their second away win of the season, should have gone in front long before they did. Johansson's second-minute save from Kelly's dipping 20-yard volley was stunning and his reaction stop to keep out Walker's header was also impressive.
Either side of those stops from the Leicester loanee, Matty Godden shot over after Johansson's initial save from a Callum O'Hare effort fell to him 10 yards out as Coventry put in a performance that belied the significance of the game.
Wing's thumping effort that came back off the post was a rare bright moment for the hosts, who competed well but lacked a cutting edge.
Mark Robins' men, who are now up to 18th, host sixth-placed Barnsley on Sunday, while the Millers could potentially be seven points from safety by the time they kick off against Blues on the same day.
- Line-upsMatch StatsLive Text
Line-upsRotherham
Formation 3-5-1-1
1Johansson20Ihiekwe6Wood21MacDonald22Olosunde16Lindsay5Wing8Wiles19Harding25Crooks24Smith
- 1Johansson20IhiekweSubstituted forSadlierat 88'minutes6WoodBooked at 90mins21MacDonald22OlosundeSubstituted forGilesat 60'minutes16LindsaySubstituted forOgbeneat 77'minutes5WingBooked at 46mins8WilesBooked at 56minsSubstituted forLadapoat 60'minutes19HardingSubstituted forRobertsonat 77'minutes25Crooks24Smith
Substitutes
- 4MacDonald9Hirst10Ladapo11Ogbene15Robertson17Sadlier26Barlaser27Blackman30Giles
Coventry
Formation 3-4-1-2
13Wilson2Østigard5McFadzean15Hyam29Da Costa6Kelly25James21McCallum11O'Hare24Godden19Walker
- 13Wilson2Østigard5McFadzean15Hyam29Da Costa6Kelly25James21McCallum11O'HareSubstituted forHamerat 77'minutes24GoddenSubstituted forGyökeresat 72'minutes19WalkerSubstituted forBiamouat 72'minutesBooked at 86mins
Substitutes
- 1Marosi4Rose8Allen9Biamou12Gyökeres20Bakayoko26Shipley28Eccles38Hamer
Referee:Jarred GillettMatch StatsHome TeamRotherhamAway TeamCoventryPossessionHome56%Away44%ShotsHome4Away12Shots on TargetHome0Away4CornersHome5Away5FoulsHome16Away14Live TextPost update
Match ends, Rotherham United 0, Coventry City 1.
90'+7'Full Time
Second Half ends, Rotherham United 0, Coventry City 1.
90'+5'Post update
Offside, Coventry City. Kyle McFadzean tries a through ball, but Viktor Gyökeres is caught offside.
90'+4'Post update
Lewis Wing (Rotherham United) wins a free kick on the left wing.
90'+4'Post update
Foul by Viktor Gyökeres (Coventry City).
90'+3'Booking
Richard Wood (Rotherham United) is shown the yellow card for a bad foul.
90'+2'Post update
Foul by Richard Wood (Rotherham United).
90'+2'Post update
Dominic Hyam (Coventry City) wins a free kick in the defensive half.
90'+1'Post update
Hand ball by Matt Crooks (Rotherham United).
89'Post update
Offside, Coventry City. Dominic Hyam tries a through ball, but Maxime Biamou is caught offside.
88'Substitution
Substitution, Rotherham United. Kieran Sadlier replaces Michael Ihiekwe.
87'Post update
Angus MacDonald (Rotherham United) wins a free kick in the defensive half.
87'Post update
Foul by Gustavo Hamer (Coventry City).
86'Booking
Maxime Biamou (Coventry City) is shown the yellow card for a bad foul.
86'Post update
Matt Crooks (Rotherham United) wins a free kick in the attacking half.
86'Post update
Foul by Maxime Biamou (Coventry City).
86'Post update
Attempt blocked. Viktor Gyökeres (Coventry City) left footed shot from the centre of the box is blocked. Assisted by Sam McCallum.
82'Post update
Foul by Kyle McFadzean (Coventry City).
82'Post update
Richard Wood (Rotherham United) wins a free kick in the defensive half.
81'Post update
Corner, Coventry City. Conceded by Viktor Johansson.
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Source: bbc.com