Keane struck in the 55th minute after a surging run by Michael Brown had cut open the Rovers defence.
Brown left two defenders in his wake before supplying the perfect lay-off for Keane who ecstatically beat Brad Friedel from 12 yards.
Only a great save from Friedel prevented Jermain Defoe adding a second goal for Spurs five minutes later.
That apart, Blackburn had by far the bulk of the possession and should have at least taken a point to extend their unbeaten run to six Premiership matches.
Blackburn's problem was a lack of imagination in midfield and they consistently failed to supply their strikers with the right sort of service.
Paul Gallagher, a scorer in his previous outing, was desperately unlucky not to add a third seconds into the second half when his snap-shot on the turn was superbly saved by Paul Robinson.
The first half had been something of a non-event although Spurs did at least force Friedel into a save, Defoe making the American keeper block with his feet after he had escaped the offside trap.
It was ironic that Spurs' winner should come during Blackburn's best spell of the game and particularly annoying for the home fans that Keane's goal came as a result of a Rovers attack.
Spurs were pushed deep into their own half and were under pressure when Brown broke superbly to set up Keane for the all-important goal.
Rovers substitutes Jay Bothroyd and David Thompson both had an impact but neither was able to find an equaliser.
Bothroyd was unlucky with a header and might have done better with a shot while Thompson was twice within a yard of a spectacular equaliser from distance.
There was an anxious moment for the Spurs defence deep in stoppage time when a free-kick on the edge of the box gave Blackburn late hope.
Fortunately for the visitors the defensive wall stood firm in the face of a shot from Steven Reid while the follow-up attempt from Paul Dickov was easily gathered by Robinson.
MAN OF THE MATCH: Michael Brown (Spurs) - Set up the vital winning goal but the former Sheffield United man was in fine form throughout.