The Rhinos were not at their best just five days after their 44-16 defeat by Warrington but showed enough flashes of individual brilliance to canter to victory.
A brace of tries from hooker Matt Diskin just before half-time looked to have put Leeds in complete command but the Londoners raised their game and outscored their hosts in the second half.
Henry Paul, starting his first game for the visitors with Thomas Leuluai on Test duty in Brisbane, was prominent in the early stages as Quins made the livelier start.
Second rower Solomon Haumono and right winger Nick Bradley-Qalilawa both reached the Leeds line but the former was held up on his back while the latter had put a foot in touch.
Leeds looked to be suffering a hangover from their heavy defeat at Warrington but there was nothing wrong with their finishing as they stormed into a 12-0 lead with two tries in 10 minutes.
Stand-off Danny McGuire, the most lethal finisher in the modern game, supported a superb break from the base of a scrum by Gareth Ellis to touch down for his 17th try of the season on 13 minutes.
And substitute Willie Poching was on hand to take the final pass from scrum-half Rob Burrow, whose searing pace and elusive footwork caused all sorts of problems for the Harlequins defence.
A solo try from full-back Mark McLinden, who demonstrated remarkable pace over 60 metres, and Paul?s conversion gave the Londoners hope at 12-6 after half an hour.
But the game took a decisive turn just before the break when McGuire turned provider for Diskin, who then took a return pass from Poching to make it two tries in four minutes and Burrow kicked his fourth conversion.
Leeds thought they had extended their lead when full-back Richie Mathers reached the line after jinking his way through the Harlequins defence just two minutes into the second half but referee Ronnie Laughton ruled he lost control of the ball in the act of scoring.
However, the visitors? defence cracked again three minutes later when Burrow and Mathers worked the ball out wide for right winger Scott Donald to squeeze over at the corner.
Burrow landed the touchline goal to maintain his 100% record with the boot to make the game seemingly safe at 30-6.
The never-say-die Londoners pulled a second try back on 50 minutes when an unlikely kick from heavyweight forward Mark Tookey was palmed back by Bradley-Qualilawa for centre Tyrone Smith to touch down and Paul kicked his second goal.
Leeds emphasised their superiority when acting captain Jamie Peacock burst through to score his second try for the Rhinos but Harlequins finished the game as they started with some delightful rugby.
Paul created a second try for McLinden and dangerous half-back Luke Dorn dashed over six minutes from the end, with Paul kicking his fourth conversion.
Leeds: Mathers, Donald, Gibson, Senior, Smith, McGuire, Burrow, Peacock, Diskin, Feather, Walker, Jones-Buchanan, Ellis. Replacements: Millard, O'Neill, Scruton, Poching.
Harlequins RL: McLinden, Gafa, Lucky Luisi, Smith, Bradley-Qalilawa, Paul, Dorn, Tookey, Randall, Mills, Hopkins, Purdham, Haumono. Replacements: Williams, Lolohea, Weisner, Budworth.
Leeds: (24) 36. Tries: McGuire, Poching, Diskin 2, Donald, Peacock. Goals: Burrow 6.
Harlequins RL: (6) 24. Tries: McLinden 2, Smith, Dorn. Goals: Paul 4.
Referee: R Laughton (Barnsley)