It has been stuttering and uneven progress, but the reigning Super League champions have at last finished a weekend in this season's top four.
Two second-half tries from last year's leading scorer, Ryan Hall, helped Leeds towards the win that took them above Hull, but they failed to convince.
For a long time at the Willows, they looked likely to join Hull and St Helens as the major scalps taken by Salford at their home this season.
"It was very hard work," said Rhinos coach Brian McClennan. "I thought Salford had the better of us, especially in that second quarter. They were all over us."
Much of the damage was done by two former Leeds players, starting with Jodie Broughton's try in the fourth minute, which came from Matty Smith's high kick and was eventually channelled to the winger by Malcolm Alker.
Leeds equalised when Danny McGuire intercepted from Adam Sidlow and Ian Kirke used his full height to stretch over the line, Kevin Sinfield surprisingly missing a simple conversion.
The rest of the half belonged to Salford, despite the absence of their main play-maker, Daniel Holdsworth, with a shoulder injury. The teenaged half-back, Marc Sneyd, made a promising full debut in his place and the ability of Ray Cashmere to get the ball out of the tackle posed a recurring threat.
They regained the lead through Ashley Gibson, like Broughton a product of Leeds' Academy, and could have been further ahead if Sidlow's try had not been disallowed for a marginal forward pass from Matty Smith.
The Reds did extend their advantage at the start of the second half through Steve Tyrer's penalty, but the Rhinos were about to hit something like their old form.
Hall's first try came from a trade-mark one-handed offload by Ali Lauitiiti and then a defensive mistake by the workhorse Alker, charging up out of the line to leave a yawning gap for Sinfield.
The Leeds captain added a penalty to his conversions after Carl Ablett was taken high and Salford finally looked as though they were out of contention when Brett Delaney's break set up Scott Donald on the right flank.
The home side continued their fight, however, with Cashmore going over from Alker's pass and Sinfield remained sufficiently concerned to put over a drop-goal for insurance.
That became largely academic when Hall claimed his second from Jamie Jones-Buchanan's pass and Sinfield added another penalty.
Salford had the consolation of scoring the best try of the match, with great handling after Jeremy Smith's break allowing Gibson to complete his brace.
"I thought the effort from the players was terrific," said their coach, Shaun McRae. "We just didn't handle their offload game in the second half."
Salford: Fitzpatrick; Broughton, Henry, Gibson, Tyrer; Sneyd, M Smith; Cashmere (Parker, 24), Alker (J Smith, 26), Boyle (Neal, 24), Littler, Sidlow (Adamson, 30), Swain.
Leeds: Webb; Donald, Delaney, Smith, Hall; Sinfield, McGuire; Leuluai (Burgess, 18), Buderus (McShane, 55), Bailey, Kirke (Lauitiiti, 24), Jones-Buchanan (Ablett, 26), Clarkson.
Referee: P Bentham (Warrington).Reuse content