Leeds (6) 22
Tries: Senior 2, Webb Goals: Sinfield 3
Salford (4) 10
Tries: Gibson, Talau Goal: Ratchford
Keith Senior had not scored a try in this season's first three matches
Leeds warmed up for next week's World Club Challenge by returning to winning ways at the expense of plucky Salford.
Keith Senior scored the champions' opening try, then ran in another to all but clinch victory late on, backed by efforts from Brent Webb and Ian Kirke.
But Salford, only 6-4 down at the break after Ashley Gibson's try, had a go.
Centre Willie Talau's try made life uncomfortable for Leeds, who suffered a bad blow when they lost winger Scott Donald with a shoulder injury.
After being pegged back to 12-10, Leeds held their nerve, Senior stretching the Rhinos clear again at 16-10 before second row Kirke made the game safe in the dying seconds.
But, despite stopping the rot after two straight defeats, at home to Castleford and last weekend at Wakefield, Leeds failed to impress against a spirited Salford outfit.
The Reds had lost prop Ray Cashmere with a calf injury in midweek and suffered another blow on the day of the game when loose forward Daniel Holdsworth pulled out with a virus.
And, for all their hard work, they still slumped to the foot of the table thanks to a third straight defeat, coupled with previous backmarkers Bradford's big Yorkshire derby win against Castleford.
Veteran centre Senior maintained his record of scoring in all 15 seasons of Super League - but otherwise it was not a performance to fill Leeds with confidence going into next Sunday evening's clash with Australian champions Melbourne Storm.
And their hopes were dealt a further blow when Donald, who scored Leeds' only try in their World Club Challenge win over Melbourne two years ago, went off after jarring his shoulder in the 15th minute.
Leeds coach Brian McClennan said:
"Scotty has jarred his shoulder. Our medical staff will review him tomorrow and Monday.
"Then we'll have an idea. At this stage I don't know whether he's doubtful or not.
"We'd like to have had a lot more cohesion but it was a hard hit-out for us. Staying in a big, tough game is better than winning by a large score. Our timing is off but the beauty is we've got experience in big games."
Salford coach Shaun McRae said:
"We lost two valuable players, who were sorely missed. But it was a terrific performance. But the effort, attitude and determination was first class, probably 10 out of 10.
"Our execution wasn't that bad either. There were a couple of opportunities that we didn't take and that was probably the difference in the end.
"We started the second half poorly and that put us under pressure. That was my only criticism of the team. Overall I'm very happy and pleased with the response. There's certainly something to build on."
Leeds: Webb, Donald, Watkins, Senior, Hall, McGuire, Burrow, Leuluai, Diskin, Peacock, Jones-Buchanan, Kirke, Sinfield.
Replacements: Buderus, Eastwood, Lauitiiti, Bailey.
Salford: Fitzpatrick, Broughton, Henry, Talau, Gibson, Ratchford, M Smith, Boyle, Alker, Parker, Sibbit, Adamson, Swain.
Replacements: J Smith, Littler, Leuluai, Sidlow.
Referee: P Bentham (Warrington).