Leeds (0) 3 Penalties: Lewis-Pratt Harlequins (14) 38 Tries: Care, Gray, Turner-Hall, Easter, Brown Conversions: Evans 4, Clegg Drop-goal: Care
Nick Easter scored Quins' fourth try
Leeds slipped closer to relegation after shipping five tries in a heavy home defeat by Harlequins.
England scrum-half Danny Care, who also kicked a drop goal, started the rot by crossing for Quins' first try.
Joe Gray got another, Nick Evans twice improving for a 14-0 interval lead, before Jordan Turner-Hall, Nick Easter and Mike Brown crossed after the break.
Leeds must now get something at Northampton in their final game on 7 May to stand a chance of staying up.
Leeds now need at least a bonus point at Franklin's Gardens. And, even then, they would require Newcastle to not take anything from their two remaining games against Bath.
Seventh-placed Quins now stand just two points behind Bath after keeping alive their hopes of the top six Premiership finish that would earn them a place in next seasons's Heineken Cup.
Quins, who have a Challenge Cup semi-final at Munster to look forward to next week, can reach Europe's premier club competition by winning the second-tier tournament.
But can they still get there by overhauling either Bath or fifth-placed London Irish, who are three points better off.
It was Headingley old boy Care, a Leeds academy product, who began his old club's woes when he took a pass from his England team-mate Easter and chipped Christian Lewis-Pratt before beating Lachlan MacKay in a race to touch down.
Three minutes later, Quins went furtehr in front when lock forward George Robson broke into the 22 and offloaded to Evans, who played an inside pass allowing hooker Gray top race over.
Leeds stand-off Adrian Jarvis missed two kicks at goal to ensure that they went in 14-0 down at the break.
But any home hopes were effectively extinguished three minutes into the second half when Quins scored their third try through centre Turner-Hall, after quick hands from Care and Gonzalo Camacho.
With Steve Thompson not coming out for the second half due to injury, and captain Marco Wentzel succumbing moments later to the half calf injury that nearly ruled him out, the game was up for the Yorkshire club.
Christian Lewis-Pratt took over kicking duties from Jarvis and got Leeds on the scoreboard after another MacKay break. But when presented with another chance, he hit the post.
Care was not so forgiving with a drop goal before Easter sprinted under the posts to secure Quins' bonus point.
Full-back Brown then ran in a 65-metre interception try from Michael Stephenson's pass before Rory Clegg converted from the touchline to complete the rout.
Leeds head coach Neil Back:
"For the first time this season it is out of our hands. Newcastle have two games.
"The fortunate thing is their opposition is Bath, who have something to fight for. They need to take 10 points to give themselves an opportunity to get into the top four.
"We're faced with a task that we hoped we wouldn't be faced. And Northampton away is as tough as it can get but, in sport, funny things can happen."
Harlequins director of rugby Conor O'Shea:
"We've given ourselves a chance of the top six. It's not in our control but it's a chance. If we continue to play like this then we can continue playing for the ultimate challenge.
"Only one team have got a bonus point up here this season, but we know on our day we can challenge people because of the way we play.
"Next week in Munster will be a fabulous experience, and we'll be ready for it."
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