Leeds’ first try came with Salford full-back Ryan Brierley in the sin-bin for a high shot.
When Sneyd tested Roberts again, the youngster stood firm and launched a Leeds counter-attack that resulted in Handley out-pacing the Salford defence to go over from his own 10-metre line and level the score.
Slack Leeds defending allowed Partington to go over from acting half-back for his first Salford try and put the visitors ahead at the break.
Leeds piled on the pressure after the break and as the Salford penalty count mounted, Handley got on the end of a neat Martin grubber kick to level it up for the third time.
Salford refused to give in and when Leeds debutant Paul Momirovski was sin-binned for a dangerous tackle on Chris Atkin, Sneyd kicked Salford ahead for the final time.
At the other end Amir Bourouh was sin-binned for slowing the play-the-ball, Martin kicked the penalty, and Lisone’s strength did the rest.
Rhinos head coach Rohan Smith told BBC Radio Leeds:
“I was really proud of the players and the work they put in to get to this point.
“We played tough, played a bit of footy at times – I really liked the calmness and composure – it didn’t all go to plan but they looked like they were enjoying the battle together.
“It felt like it was a two-hour game – there were a lot of really long stoppages – it would’ve been good if we weren’t stopping the game for blokes to do their boots up.
“It’s an atmosphere killer – you can go and make another pot of tea if you’re at home watching that.”
Salford coach Paul Rowley:
“Nene [Macdonald] has been in hospital with his boy all day and wasn’t going to play.
“His boy’s been really poorly so I’m just glad his little fella is home and well. It was a really good shift from him to step up and be a team player.
“I don’t think there was much in the game. I don’t think we were hanging on and for large parts we were controlling the game and were comfortable. I’m proud of the lads.”
Leeds: Miller; Roberts, Newman, Momirovski, Handley; Croft, Frawley; Oledzki, Ackers, Donaldson, Goudemand, Martin, Smith.
Interchanges: Bentley, O’Connor, Lisone, Sangare.
Sin-bin: Momirovski (57).
Salford: Brierley; Hankinson, Macdonald, Lafai, Cross; Cust, Sneyd; Ormondroyd, Bourouh, Singleton, Watkins, Stone, Partington.
Interchanges: Atkin, Shorrocks, Wright, Hellewell.
Sin-bin: Brierley (13), Bourouh (64).
Referee: Aaron Moore
