Veteran centre Keith Senior grabbed two tries to maintain his record of scoring in every Super League season to give the Rhinos the edge against a spirited Salford outfit, who slumped to the foot of the table after a third defeat in as many games.
It was not a performance to fill Leeds with confidence going into next Sunday's meeting with Australian champions Melbourne Storm and their hopes were dealt a further blow with winger Scott Donald picking up a shoulder injury.
Still reeling from surprise back-to-back defeats by Castleford and Wakefield, the Rhinos got off to an ideal start with an eighth-minute try from Senior.
Second-row Jamie Jones-Buchanan, who had been hauled down just short of the line moments earlier by Reds full-back Karl Fitzpatrick, produced a superb offload to get Senior over the line.
Kevin Sinfield's conversion made it 6-0 but it went downhill from there for the Rhinos as Salford, looking for their first win of the season, rallied magnificently.
Donald, who scored Leeds's only try in their World Club Challenge win over Melbourne two years ago, went off after jarring his shoulder in the 15th minute, forcing coach Brian McClennan to switch Jones-Buchanan from the pack in a reshuffled line-up.
The champions had plenty of possession but met much sterner resistance from the visitors, who for long periods looked capable of repeating last year's shock win at Headingley.
Former Leeds three-quarter Ashley Gibson, who fumbled Sinfield's early high kick and failed to take an awkward pass from Matty Smith with a clear opening in the Rhinos' defence, recovered from his earlier blemishes to bring the Reds back into contention. He got into his stride down the right flank and superbly fended off full-back Brent Webb to register his first try for his new club.
Stefan Ratchford was unable to add the conversion but, at 6-4, Salford were firmly in the game.
However, the Reds, without Australian duo Ray Cashmere and Daniel Holdsworth, put themselves under pressure with a series of handling errors in the early part of the second half and Leeds made them pay. When Rob Burrow hoisted a high kick on the last tackle, Webb was the first to the ball and brought it down for the Rhinos' second try.
Sinfield's second goal made it 12-4 but the Reds almost scored the next try when Fitzpatrick chased Matty Smith's kick only to be beaten by the dead-ball line.
However, Salford were not to be denied and on the hour centre Willie Talau pounced for a try after a rare handling error from Danny McGuire and Ratchford's successful conversion cut the gap to only two points. Senior spared the champions' blushes, pouncing for his second try after 66 minutes when winger Ryan Hall palmed the ball back from Sinfield's lofted kick, and second-row Ian Kirke grabbed a try in stoppage time following Greg Eastwood's break but they did little to lift the spirits of the 12,700 crowd.
Leeds Rhinos: Webb, Donald, Watkins, Senior, Hall, McGuire, Burrow, Leuluai, Diskin, Peacock, Jones-Buchanan, Kirke, Sinfield. Substitutes: Buderus, Eastwood, Lauitiiti, Bailey.
Salford Reds: Fitzpatrick, Broughton, Henry, Talau, Gibson, Ratchford, M. Smith, Boyle, Alker, Parker, Sibbit, Adamson, Swain. Substitutes: J. Smith, Littler, Leuluai, Sidlow.
Referee: P Bentham (Warrington).