The Whites started like a house on fire and went ahead in the first half through Jack Harrison, but were pegged back after the break with free-kick expert James Ward-Prowse finding the back of the net for Southampton.
On most of the statistics It was an even game and it could turn out to be an important point for Leeds come the end of the season as they continue to battle to stay out of relegation trouble.
With Burnley and Watford both losing they are now eight points clear of the bottom three.
The value of the point was not lost of United boss Marsch.
He said: "It was a real fight. I know their coach and they are a good team. We knew that second balls would be a premium.
"It was a tight game and trying to find chances was not easy.
"It was often quite ugly and it was about turning little things into chances.
"We are trying to take more of our chances. We are not quite as effective in the last third as I'd like us to be.
"For the most part we defended well and played with confidence
"Clearly our confidence is getting better and overall I'm satisfied with a point.
"I think we are only going to get better and in terms of clarity of how we want to play it was one of our better performances."
Marsch was delighted with the first team comebacks from defender Liam Cooper, who played 90 minutes, and Kalvin Phillips, who came on to play the last half-hour in midfield.
He added: "Liam was fantastic. He’s such a big presence in our team.
"And then you can see the quality from Kalvin. That’s a big step for us as a team and for them.
“And having them more at 100 per cent fitness and sharpness will be massive for us.”
Marsch has previously spoken about the need to start well and he could have seen his side go ahead several times in the opening five minutes.
Dan James was almost through onto one of a number of effective Rodrigo through balls in the early stages, only for a last desperate tackle by Mohammed Salisu to deny him. From the resulting Jack Harrison corner Diego Llorente sent his header inches wide.
More shots were blocked by desperate Southampton defending before Mateusz Klich had time to weigh up a shot on the edge of the box, but could only send the ball wide.
Southampton's first sight of goal saw Mohamed Elyounoussi shoot straight at home keeper Illan Meslier when he was found in space in the area.
It was quickly down the other end from that chance with James again put away by Rodrigo only to see his shot well saved by Saints keeper Fraser Forster.
Harrison was inches away from an unusual goal as his seemingly mis-hit corner came back off the post. The ball ended up in the back of the net after a further scramble, but Rodrigo was correctly judged to have fouled a Southampton defender.
In what was cracking first half-hour it was then the visitors' turn to go close through Che Adams' shot that was deflected over off Llorente.
A goal had to come and it was the Whites who got it on 29 minutes when Raphinha did well to get a cross in from right on the bye-line, Forster could only tip it on and Harrison came in to poke the ball home.
It was not the cue for United to go on and dominate as their opponents finished the first half the better. Adams turned cleverly in the area only to see his low shot superbly saved by Meslier then equally well cleared by Stuart Dallas. Then newly England capped Kyle Walker-Peters shot wide from the edge of the box.
Southampton's improved work continued at the start of the second half when they were fortunately awarded a free-kick 20 yards out and the deadly Ward-Prowse sent in a superb free-kick that found the net despite Meslier getting a hand to it.
They could have been ahead two minutes later as Armando Broja sent a close range effort wide, but Leeds responded and after combining well with Rodrigo from half-way Raphinha chipped the ball over.
Meslier was forced into two more saves to deny Ibrahima Diallo as the visitors looked to turn the screw.
The game went through a stop-start phase with several injuries breaking up play and Southampton's domination ended. With Phillips on to boost the midfield Leeds got a bit more control back in their play and they could have scored as Dallas's volley had to be saved by Forster when he met a cross by another of the subs, Joe Gelhardt.
Neither side were good enough to fashion clear chances in the final 20 minutes although United had a big shout for a penalty turned down by referee Anthony Taylor after Gelhardt went down in the area. It was one of those "seen them given" decisions, but not to be this time.
Saturday, April 2, 2022
Leeds: Meslier; Ayling (Struijk 89), Llorente, Cooper, Dallas; Forshaw, Klich (Phillips 66); Raphinha, Harrison, Rodrigo; James (Gelhardt 58).
Southampton: Forster; Livramento, Bednarek, Salisu, Walker-Peters; Romeu (S Armstrong 64); Ward-Prowse, Elyounoussi, Diallo; Broja (Long 90), Adams (Tella 87).
Referee: Anthony Taylor