Watched by England manager Roy Hodgson, the young striker scored his 25th and 26th goal of the season in all competitions, enough to hold off a late consolation from Sandro
The England hopeful met Andros Townsend's cross to head home the opener in the 34th minute at Loftus Road before pouncing on some poor defending in the second half to double Spurs' advantage, taking him to 26 goals in all competitions this season.
Former Tottenham midfielder Sandro got one back for the relegation-threatened hosts shortly afterwards with a fine finish past Hugo Lloris but Spurs held on to move ahead of Southampton into sixth place.
|VIEW FROM LOFTUS ROAD
|By Harry Sherlock
The away fans breathed a collective sigh of relief after a nervy Tottenham performance at Loftus Road. Harry Kane was again the hero for Mauricio Pochettino's men, scoring twice under the watchful eye of Roy Hodgson.
QPR did their best to spoil the party, Sandro scoring against his old club, but Pochettino has instilled a philosophy based on resilience and this was again in evidence in west London.
It may not have been pretty but the Argentine made a point of embracing every single one of his players as they headed down the tunnel. In the race for the top four, this could be a huge three points.
QPR, meanwhile, need to start winning - and quickly - if they are to avoid the dreaded drop.
Rio Ferdinand and Mauricio Isla returned to the QPR starting XI, while Ben Davies replaced Danny Rose at left-back for Tottenham.
QPR striker Bobby Zamora looped a header against the crossbar inside the first minute as his former club made an initially sluggish start but it did not take long for Tottenham to find their rhythm and Rs goalkeeper Rob Green made a magnificent point-blank save to deny Kane from Kyle Walker's right-wing cross.
Walker was almost culpable for the hosts taking a 20th-minute lead when Austin turned his ill-advised backwards header goalwards but Lloris responded with a superb reaction stop.
Zamora and Austin combined for Matt Phillips to thump wide from inside the area as QPR grew in confidence as an attacking force. Austin came closer still in the 29th minute as he touched the ball beyond the Tottenham defence and clattered a left-footed shot against the crossbar.
QPR rued those missed chances as Kane headed in from Andros Townsend's floated free kick, capitalising on disorganised home defending and Green coming out to leave himself stranded.
Isla had penalty claims rejected when he went down under a challenge from Lloris, who saved once more from Austin in first-half stoppage time after Green kept out Walker's deflected drive.
Tottenham began the second half brightly, with Christian Eriksen curling a strike against the post and Kane blasting the rebound off target. Townsend passed up a 49th-minute opening when Steven Caulker carelessly gave away possession, while Eriksen failed to pick out Nacer Chadli when Tottenham took QPR apart on the break.
Direct play up towards Zamora continued to prove fruitful for the Rs and the targetman drew a sharp near-post save from Lloris in the 57th minute.
Zamora's strike partner, Austin, was an unlikely hero at the other end two minutes later when he cleared Eriksen's shot off the line.
Midway through the second half, Tottenham's pressure eventually told as Kane sprung a sorry excuse for a QPR offside trap and coolly rounded Green to slot home.
Sandro drilled home from just inside the box to set up a grandstand finish, during which Austin led furious protests for a penalty when Nabil Bentaleb blocked his close-range shot with an arm.
Referee Craig Pawson was again unmoved, allowing Mauricio Pochettino's team to make it back-to-back Premier League wins following their League Cup final loss to Chelsea.