Leeds were given a fright by Super League rivals Salford before booking their place in the quarter-finals of the Carnegie Challenge Cup.
The City Reds held their own in the first half, going in 6-6 with last year's beaten finalists, before Rhinos crossed twice through Ben Jones-Bishop and Shaun Lunt to run out 16-10 winners.
The battling Reds had gone ahead with a Lee Jewitt try, cancelled out by Brent Webb just before the interval.
Salford, playing against a strong wind in the first half, took a shock eighth-minute lead after a storming run by Jodie Broughton against his old club.
Jewitt took Wayne Godwin's pass to plough over from short range for his first try since scoring against Leeds last July, with Daniel Holdsworth booting the straightforward conversion.
The Rhinos recovered to pile the pressure on the Reds but squandered several chances.
Chris Clarkson was put through by Kevin Sinfield but the skipper tossed away a certain try by ignoring Webb in support.
Jones-Bishop went over but was recalled for a forward pass and then Zak Hardaker was denied a try from Danny McGuire's kick by a desperate Luke Patten clearance.
Carl Ablett then dropped the ball under pressure over the Reds line after slick handling by McGuire and Webb.
Salford were under the cosh with solid defence preventing Darrell Griffin barging over before the Reds line was finally breached four minutes before the break.
Lunt's grubber kick caught Salford off-guard and Webb was the quickest to react with Sinfield landing the conversion to make it 6-6.
Salford lost Chris Nero early in the second half with an arm injury but Ashley Gibsonsummed up their spirit with sterling defence.
The Reds regained the lead after 51 minutes when Broughton sprinted on to Holdsworth's well-placed kick for his fourth try of the season.
Holdsworth was just off-target with the touchline conversion but Leeds drew level 16 minutes from time.
Jamie Peacock did well to release the ball in a tackle and Sinfield's kick was fumbled by Broughton for Jones-Bishop to score a scrambled try.
Sinfield missed the conversion to stop his side going ahead for the first time.
Salford's relief was short-lived with McGuire's dancing run enabling Lunt to go over after 71 minutes and, this time, Sinfield made no mistake to extend the lead to six points.
The Reds refused to concede defeat and Sean Gleeson went close but Leeds held on