Aaron Mclean's 33rd-minute finish was the bright point of a scrappy first half at the Ricoh Arena.
Coventry, who failed to register a shot on target during the opening 45 minutes, were much improved after the break and came close to equalising on several occasions but efforts from Richard Wood and Aron Gunnarsson were cleared off the line.
Hull held on to make it 14 games without defeat on their travels, beating the previous record set during the 1948-49 season.
It was announced before the game that Coventry boss Aidy Boothroyd will climb Mount Kilimanjaro to raise money for Comic Relief, and his side certainly have a mountain to overcome after the result extended their poor run to only one win in the last 16 Championship matches.
Keiren Westwood returned in goal for Coventry after missing the midweek draw at Doncaster due to a hip injury.
Hull also made one change, with Tom Cairney replacing Nick Barmby.
The majority of the first half got bogged down in midfield as both sides struggled to create chances.
Gunnarsson's long throws gave Hull a few hairy moments, while in between Robert Koren should have really done better than glance his near-post header wide from Liam Rosenior's cross.
The only goal of the game arrived when Matty Fryatt chased down a long ball forward before teeing up strike partner Mclean, who arrived from nowhere to thump a low shot past Westwood.
Coventry enjoyed their only real spell of pressure either side of the hour mark and might have levelled on three separate occasions.
Wood had a header cleared off the line before Gunnarsson's shot from the edge of the box struck a defender a yard in front of the goal. Wood then had another effort hacked off the line.
However, Boothroyd's side failed to build on those chances and should have fallen further behind when Mclean went through one-on-one but Westwood made a superb block.
Coventry's momentum had gone and the game petered out during the remainder of the second half.
Anthony Gerrard headed over the crossbar and Fryatt worked Westwood as Hull threatened again late on.