A very balanced match saw both teams create chances for Molineux in a close-to-end fight.
But Podence struck just before half-time to give Wolves a much-needed lead.
The second half was similar to the first as Wolves found openings but were unable to put them on the count, while Southampton scored a handball goal and hit the crossbar.
But Wolves clung to the result to register their first league victory of the season, on the sixth attempt.
Bruno Lage made three changes from the midweek draw with Bournemouth and stuck to the 4-3-3 formation.
Sasa Kalajdzic entered straight into the starting XI on his Wolves debut, while Rayan Ait-Nouri and Podence also made the squad, as did Nelson Semedo, Goncalo Guedes fell to the bench.
Raul Jimenez was named as a substitute but came off during the warm-up and was replaced by Chem Campbell before kick-off.
Young full-back Hugo Bueno has been named as a substitute to give Wolves more defensive options. Centre-back Yerson Mosquera has not been included.
Deadline day signing Boubacar Traore was not involved as he is due to fly to England and join the team in the coming days.
Ralph Hasenhuttl has made a change for his Southampton side who beat Chelsea 2-1 in midweek.
Romeo Lavia, who scored in that game, was not involved with the team at all and was replaced in the starting XI by Joe Aribo.
Southampton also named three signings on deadline day from the bench in former West Brom loanee Ainsley Maitland-Niles, Juan Larios and Samuel Edozie.
Before kick-off, Molineux paid tribute to former manager Sammy Chung, who died aged 90 earlier in the week.
A good first move saw Podence do well to keep the ball in play before whipping in a cross for 6-foot-7 striker Kalajdzic. However, Southampton faced danger with the new striker in hiding.
Wolves had more joy on the left side once they quickly switched play, and a one-two between Ait-Nouri and Podence saw the former run into the box. He then forced Gavin Bazunu into a save at his nearest post.
The game’s best chance came after 14 minutes when Wolves burst in numbers. Matheus Nunes collected the ball from under his feet but eventually released Pedro Neto on his right, despite Ait-Nouri being free on the left. Neto cut inside but shot wide with his left boot.
The visitors still carried a threat, however, and should have scored through Aribo. Striker Che Adams did well on the right and his low cross was set for Aribo to finish from two yards out, but Ruben Neves made a superb recovery tackle to deny it.
Armel Bella-Kotchap then had a free header from a corner but deflected it wide, in a huge let off for Wolves.
At the other end, Kalajdzic was making himself a nuisance. A corner kicked in and the hulking striker stretched for it and headed wide wide.
Sloppy passing slipped into Wolves play as Southampton threatened to take control. The home fans continued to support the team, but the officials’ frustration and individual mistakes were evident.
Ait-Nouri did well, however, when he came forward and aimed a low cross towards Kalajdzic. The striker was in acres of space but Southampton did well to clear him just past him.
Half a chance then went to Adam Armstrong when the ball was tipped at him in the box, but it burst into flames.
On the stroke of half-time, Wolves then took the lead. A quick break saw Nunes appear with the ball on the right and his low cross left Podence with just the goalkeeper to beat, and he tossed it over Bazunu to give Wolves the much-needed advantage.
That goal was the last major action of the half as Wolves took a 1-0 lead into the break.
As the teams emerged for the second half, Wolves were dealt a blow as Kalajdzic was replaced by Guedes. The striker injured his knee before the break and looked uncomfortable, but he continued to play. However, he was then sent off at half-time.
Guedes was almost instantly on the scoresheet when Wolves burst in and Neto appeared with the ball on the right. He found Guedes inside the box in space, but his first touch saw the ball fly under his boot and away from danger.
Moments later, Guedes ran for goal but didn’t get the ball off his feet, with a shot opportunity and a pass to Podence both available.
Wolves were finding space and good play from Nunes saw him free Neto down the right. He reached the goal line and had an easy cross for Podence to have a tap at the back post, but instead puffed the ball up behind for a goal kick. He was visibly furious with himself.
On the next attempt, once Neto was released once again, he nailed his cross well and Guedes was inches away from meeting it.
There were hearts in their mouths when Neves delivered a free-kick from the edge of the box and dead-ball specialist James Ward-Prowse stood over it – but his effort was direct on Jose Sa.
Just after the hour mark, Southampton had the ball in the net when Aribo crossed from inside the box and Adams brought it in from close range. However, referee John Brooks rightly gave a free kick as Adams used his arm to direct the ball into the net.
Moments later, however, Adams rose high in the box to head for goal and his effort hit the crossbar as Saints pushed to equalise.
After surviving some pressure from Southampton, Wolves created openings of their own. Neto was sent several times down the right as the hosts brought the ball into the box, but they missed the final ball.
Wolves fans showed their frustration when Nunes ran forward and played Neto down the right, but the winger cut inside again and lost the ball with good luck at his mercy.
A free-kick almost resulted in a second goal when Max Kilman headed for goal, but it was cleared just past Nunes who was flying at the far post.
Saints kept pushing and forced Wolves into last-minute tackles and blocks, with Kilman standing out for his bravery and commitment.
The final four minutes of added time were nerve-wracking but Wolves hung on to their slight lead to take the three points.
Wolves: Sa, Jonny, Collins, Kilman, Ait-Nouri, Neves, Nunes, Moutinho, Podence (Traoré, 82), Kalajdzic (Guedes, 45), Neto (Hwang, 82)
Subs not used: Sarkic, Semedo, Bueno, Gomes, Ronan, Campbell.
Southampton: Bazunu, Walker-Peters, Bella-Kotchap, Salisu, Perraud (Edozie, 73), Diallo (Djenepo, 56), Ward-Prowse, Elyounoussi (S. Armstrong, 56), Aribo (Maitland-Niles, 73), Armstrong (Mara, 83)., Adams.
Unused submarines: McCarthy, Larios, Lyanco, Walcott.
Wolves 1 Southampton 0 – Report