The game was only a minute old when Matty Robson latched on to a cross from JP McGovern to give Carlisle the lead over a Coventry side looking to extend a record of six away wins in a row.
Ninety five minutes of football later it was still the only thing separating the sides.
t was a huge improvement on the Blues last outing when they were beaten 4-0 by Swindon.
Liam Noble and Lee Miller both spurned chances to extend United's lead, while two shocking misses by Coventry's Leon Clarke will have been a bitter pill for away fans to swallow.
Carlisle are now 17th in League One, nineteen points above the relegation zone.
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John Davidson, who grew up in Newcastleton, was killed while trying to arrest a suspect last week.
Police are looking at CCTV footage after money was taken from her bag in a shop in the town.
Four other people have been released without charge, after Kevin Slater was found dead outside a property on Borland Avenue.