Lambe struck against the run of play a minute from half-time to leave Rovers bottom of the table and on the verge of the drop with only three games to go.
However, a second yellow card of the night in an amazing 14 added minutes at the end ensured Lambe missed out on the celebrations.
“I have seen certain players become men here and I am proud of them,” said Murray as his side went eight points clear of the drop with three games left.
“That was a massive three points and we knew it would a massive step. But the manager in me says we still have three to go and we want to finish the season on a winning run. Our performances have deserved it.
“They will need some recovery in the next few days as there are some absolutely shattered bodies in there.
“Knowing this league you can never count your chickens. But we’ve made it a tad easier for the run-in. Now the boys must work harder and express themselves.
“It was probably the worst game of football I’ve ever watched in my life.
“But we knew what it was going to be. We knew it would be scrappy and a battle in such a big game. But the tension from both sides was ridiculous.
“When our backs were against the wall it showed what a great team spirit we’ve built here.”
He added: “I thought Reggie was superb, though I was disappointed with his sending off. I hope the referee will look at it again as he got it totally wrong.
“I sent Reggie in there to clam things down, yet he’s pulled him out and shown him a second yellow card. He wasn’t trying to be aggressive and I am glad it didn’t cost us.
“The 14 added minutes was incredible. There was nothing we could do but see it out.”
Mansfield came out the blocks fastest and Owain Fon Williams had to deny Vadaine Oliver with his legs after just 20 seconds.
But after 15 minutes the visitors, with nothing to lose, took complete control and Rory Donnelly wasted a chance from eight yards when he sidefooted wide.
But just before the break Jamie McGuire ran at Rovers and found Oliver in the box who set up Lambe for a neat low finish from 12 yards just wide of the keeper’s fingertips and inside the right post.
Mansfield defended magnificently after the break, Sasha Studer denying Donnelly and Jennison Myrie-Williams and, despite the kitchen sink coming at them in an incredibly tense finish, they hung on to what they had.
Tranmere boss Micky Adams said: “It’s the story of our season. We haven’t scored enough goals. We have dominated another game territorially but haven’t scored.
“It is just disappointing. We just can’t find a way through. It has been a recurring theme all season.
We haven’t showed enough quality in the final third.
“If the game was based on territory and possession we win it comfortably. Mansfield had just two shots.
“We tried to create opportunities, we got the ball wide and in good areas. But we didn’t test the goalkeeper despite trying enough combinations.
“There wasn’t a lack of effort, the players were well up for the game and knew the importance of it.
“It was a real kick in the teeth to go one nil down just before half-time.
“Although Mansfield started really brightly, we rode the storm and then came into it. We had a couple of chances that we didn’t put away. To go in behind was disappointing.
“I’m not in the excuses game, it is not good enough. If you analyse everyone who has played up front this season, including people no longer at the club, it hasn’t been good enough. We haven’t scored enough goals.
“To win games you have to have goalscorers and we haven’t had that.
“We have to find ways of doing it. Our quality has to be spot on from set plays for the final three games. We have to go again on Saturday.
“The fans were terrific and made a lot of noise. They made a terrific atmosphere.”