Aaron Mclean's 33rd-minute finish was the bright point of a scrappy first half at the Ricoh Arena.
It 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 Keiren Westwood.
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.