Defeat would have left the defending champions facing the likely prospect of having to win the million pound game to stay in Super League.
When they trailed 6-4 at half-time, to a team on a 16-game losing run, that seemed a distinct possibility, but two moments of inspiration secured a priceless two points and a win that carried Leeds a step closer to top-flight survival.
In the third quarter, after a long spell spent defending near Leeds’s line, stand-off Liam Sutcliffe landed a 40-20 kick which got the visitors on the front foot for the first time since the interval.
In the resulting set a strong run and quick play-the-ball by Rhinos’ best player on the day, full-back Jack Walker, led to Matt Parcell going over for a try which edged them ahead.
With four minutes left Sutcliffe made a break down the right and his pass inside sent Richie Myler over for the clinching try.
Both second-half touchdowns were converted by Sutcliffe, but the game was more tense than the 10-point margin suggests.
Krisnan Inu spilled the ball over Leeds’s line early in the second half when a try would have opened a two-score gap.
With Leeds ahead by four, Jimmy Keinhorst made a remarkable tackle to keep Widnes’s Joe Mellor out and in the set before Myler’s try Patrick Ah Van had a clear run to the line from Inu’s pass, but he knocked on.
In the first half Leeds went ahead when Luke Briscoe raced 70 metres after Myler had pounced on a loose ball, but Widnes rallied through a close-range Tom Olbison touchdown which Inu converted.
It was a poor-quality contest, between two teams clearly lacking in confidence, but one of those occasions when the result was all that mattered.
Leeds director of rugby Kevin Sinfield was a relieved man after the final whistle, but felt his side deserved the points for their strong defensive effort.
“I thought it was a really good game,” he reflected
“I thought Widnes threw some things at us and I thought they played pretty well.
“I really liked our attitude, the way we stuck in there, but it was certainly tense and I’m just pleased we were able to come through it.”
Rhinos had been beaten 38-36 by Hull KR in their previous game and Sinfield added: “Defensively we were a whole lot better than last week, which is something we’ve worked on this week.
“We copped a fair amount of penalties, especially on our own line and had to defend and back up and look after each other and we were able to do that.”
Rhinos remain second in the Qualifiers, two points behind Salford Red Devils who they play host to on Friday and two ahead of fourth-placed Toronto Wolfpack.
The top-three will secure a place in Super League for next season with the final spot being decided by a play-off between the fourth- and fifth-placed teams.
After Salford, Leeds complete their campaign with two games against Championship opposition, visiting Halifax before Toronto travel to Headingley in round seven.
Two more wins should be enough to secure safety and Sinfield said: “Three wins from four looks a lot better than two from four, but there’s still a bit of work to do.”
Widnes Vikings: Mellor, Ah Van, Inu, Runciman, Buckley, Lyons, Finn, J Chapelhow, White, Houston, Hauraki, Leuluai. Substitutes: D Walker, Gubb, Olbison, Wilde.
Leeds Rhinos: J Walker, T Briscoe, Keinhorst, Moon, L Briscoe, L Sutcliffe, Myler, Crosby, Dwyer, Singleton, Jones-Buchanan, Ferres, Thompson. Substitutes: Parcell, Peteru, Smith, Walters.
Referee: C Kendall (Huddersfield).