Harrogate 20 Nuneaton 42
Fly-half Gareth Cull contributed 22 points as battling Nuneaton followed up their home win over Moseley with a thundering victory at Claro Road.
With three matches to go, Nuns now need to bridge an eight-point gap beyond Harrogate and Bracknell to reach safety from relegation.
Full-back Matt Cardey set them on their way with a fifth-minute try and Nuns were 15 points up by the 20th minute when Cull chased his own kick ahead for their second touchdown.
But Harrogate drew level when Lee Cholewa added a penalty to conversions of tries by speedy winger Jamie Tapster and full- back Ed Smithies before Cull's second penalty gave Nuns an 18-15 interval lead.
Centre Jody Peacock's try extended that lead, Cull converting, and though fly-half Cholewa replied with a Harrogate try Nuns dominated the final quarter.
Cull put Fijian winger Laka Laka away for a fourth try, converted, added a drop-goal and then converted Peacock's second try.