Kane, who was nurtured by QPR’s head coach when in the Tottenham youth team, found the net either side of half-time – his 25th and 26th goals of the season – in a pulsating affair that saw Christian Eriksen and Charlie Austin hit the woodwork, as well as QPR have two strong penalty appeals turned down.
Sandro scored late on against his former club but it was not enough as the west Londoners lost by a one-goal margin for the 11th time this season and remain three points adrift of safety.
Tottenham, meanwhile, move above Southampton into sixth after victory, three points off Manchester United in fourth.
Kane sent a warning out to the QPR defence inside five minutes when he latched onto a Kyle Walker cross but his header was brilliantly saved by Rob Green.
Roy Hodgson was in the stands to check out the progress of a man he now deems ready for a call-up but it was another English striker, Austin, who caught the eye midway through the half.
QPR’s 15-goal man was denied by close range from Hugo Lloris on 19 minutes after a poor Walker back-header was seized upon by the striker.
He had an even better chance nine minutes later but rattled the crossbar from 15 yards.
That miss would prove costly as on 33 minutes as Kane showed Austin how it should be done, heading home an Andros Townsend free-kick amid confusion between Green and his QPR defence.
Undeterred by the goal QPR continued to create good opportunities and they were left stunned on 38 minutes as Mauricio Isla was caught in the area by a reckless Lloris, who came flying out of his goal, but referee Craig Pawson was unmoved.
Eriksen had a quiet opening 45 minutes but burst onto the scene early in the second with a ferocious 25-yard drive that came cannoning back off the post.
Townsend then went close from 20 yards after a mistake by Steven Caulker before Bobby Zamora tested Lloris with a half volley from a tight angle.
Austin then had to become a goal-saver rather than goalscorer, clearing a Eriksen shot off the line.
The end-to-end nature of the game always threatened more goals and it was Kane who seized the opportunity on 66 minutes.
Rio Ferdinand tried to play Kane offside near the halfway line but got his bearings wrong as the young striker got on his shoulder and burst through on goal from a Ryan Mason pass.
There was an air of inevitability as he went one-on-one with Green, coolly rounding the goalkeeper and tapping the ball into the empty net.
QPR responded in the same manner as they did in midweek against Arsenal to going 2-0 down by hitting back within five minutes.
Sandro, who made 81 appearances for Tottenham, found space on the edge of the area and planed a lovely drive into the bottom corner.
The goal lifted the crowd at Loftus Road and they were left seething just three minutes later when Nabil Bentaleb blocked a goal bound Austin drive from 10 yards with his hands as he lifted them to cover his face.
However, once again referee Pawson rejected QPR’s strong appeals for a spot kick and Spurs hung on to continue their pursuit of Champions League football.
QPR: Green (6), Onouha (7), Caulker (6), Ferdinand (5), Suk-Young (6), Isla (7), Sandro (7), Henry (6), Phillips (6), Austin (7), Zamora (6).
Subs: Grego-Cox (6), Hoilett (6), Wright-Philips (6)
Tottenham: Lloris (7), Walker (7), Dier (6), Vertonghen (6), Davies (6); Bentaleb (6), Mason (7); Chadli (6), Eriksen (7), Townsend (7); Kane (8).
Subs: Dembele (6), Lamela (6), Stambouli (6)
Man of the Match: Harry Kane