Kane's first-half header and Keogh's late penalty proved enough to see off Hull on the day the Lions said farewell to club legend Barry Kitchener, who died a week ago aged 64.
A service and minutes' applause were held before the game, in which Millwall wore special white kits in memory of their former centre-half.
They then went on to stage the most fitting tribute possible with a battling display one-club 'Kitch' would have been proud of.
Kane and Keogh's goals eased Millwall's relegation fears and secured the Lions' 1,000th home league win, a milestone they had been trying to reach since their last success on Boxing Day.
They also inflicted a fifth straight defeat on Hull, whose play-off hopes are fading fast.
Yet Hull made the livelier start and should have opened the scoring in the 23rd minute when Richard Garcia was played in by Corry Evans, but the Australian forward's weak effort was kept out by the legs of Maik Taylor.
Instead it was Millwall who took the lead just two minutes later when James Henry's corner from the left was bravely nodded in at the far post by Kane.
The busy Kane should have doubled the advantage after half an hour when Hamer Bouazza's cross was helped on by Keogh, but the on-loan Tottenham youngster, at full stretch, could only poke the ball over from all of three yards out.
Moments later Kane's shot appeared to be blocked by the arm of Andy Dawson and, while Millwall appealed in vain for a penalty, Josh Wright blazed the rebound just over.
Kane was denied again just after half-time when his header, from another Henry corner, was cleared off the line by Sonny Bradley.
For Hull, Tom Cairney's drive was well saved by Taylor, Evans shot too high and Robbie Brady planted a header over the crossbar.
But the Tigers were largely kept at bay by centre-halves Shane Lowry and skipper Paul Robinson who, in true Kitchener style, were determined to keep a clean sheet
And Millwall made the game safe in the 81st minute when Liam Cooper fouled Keogh in the area and the striker picked himself up to roll in the spot-kick and cap a memorable day for the Lions.