A must-win clash in the race for the Europa League, they got the job done despite being far from their best.
Podence's header - his first Wolves goal after his £17million move from Olympiacos - came shortly before the break, and Otto stopped the anxiety with a smart finish.
Nuno Espirito Santo's side have leap-frogged Tottenham back into sixth, ahead of Sunday's enormous season-ending game at Chelsea.
The performance was not anything to shout about - but the three points were just what the doctor ordered.
Wolves underwhelmed for the majority of this match, the last league outing at Molineux of this massive season, but turned on the style for their two goals.
Joao Moutinho came up with an absolute peach of a pass in the build-up to the opener - Podence, who was busy again, getting off the mark.
Then, Adama Traore tore through the Eagles backline for the second, which was superbly tucked away by Otto.
Palace will feel hard done by, but once Wolves had the two-goal cushion, the result was never in any doubt.
Nuno's men are now preparing for Chelsea, knowing a win will seal Europa football once more.
Wolves have also surpassed their points tally from last season - 59 compared to 57. One last push.
Nuno made three changes to the side which agonisingly drew 1-1 at Burnley last week.
Matt Doherty - the victim of the controversial last-gasp Turf Moor penalty call - came back in along with Otto and Leander Dendoncker.
Surprisingly, Dendoncker was in defence, with Romain Saiss dropping to the bench. Podence, meanwhile, made his third start in succession in attack - a show of faith in the January signing.
Palace had a couple of notable absentees in Patrick Van Aanholt and Luka Milivojevic - both injured - and because of the former missing out, young Tyrick Mitchell made his first league start at left-back.
He had the unenviable task of keeping Wolves' frighteningly-fast winger Traore quiet, so there was potential for a baptism of fire.
Traore, interestingly, had his right arm rubbed in Vaseline before kick-off in an attempt to stop the Eagles' defenders from pulling his shoulder out of place for the fifth time this season.
The visitors began fairly sharply, seeing most of the ball and not looking like a team that had lost their last six matches.
Wolves had top scorer Raul Jimenez shoot straight at Vicente Guaita from a tight angle after some tenacious work, holding off a challenge from Mamadou Sakho.
Still, it was Palace who were, in the main, keeping the hosts penned in as they enjoyed the lion's share of possession in a rather uneventful first 20 minutes.
But the away side would soon be forced into a change as Sakho pulled up with what appeared to be a hamstring issue. Cheikhou Kouyate took his place.
Wolves did not take advantage of the enforced switch, though, as Roy Hodgson's men continued to be the more convincing of the two teams.
They had a glorious opportunity to take the lead on the half-hour mark, too.
Willy Boly had the ball stolen off him by Wilfried Zaha, and he released Jeffrey Schlupp, who broke into the box and dragged his effort beyond the far post. He really should have scored.
Palace almost seemed like they had a man advantage as they were all over Wolves.
As it turned out, though, against the balance of play, Nuno's charges took the lead. On the whole, it was a very flat half from Wolves, but a moment of magic from Moutinho unlocked the Eagles.
His beautiful lofted pass released Doherty, who squared it across goal for Podence - the smallest man on the pitch - to nod in and open his gold and black account.
Palace will have, undoubtedly, felt a great sense of injustice, and their frustration increased as they made a slow start to the second period - Zaha losing his footing a few times.
Podence, despite his lack of height, fancied his chances of scoring another header, too, as he tried to get on the end of a Traore cross, but Joel Ward got there first.
As the away side became increasingly agitated, Wolves almost doubled their advantage. Traore surged into the area and stung the palms of Guaita, with the ball falling kindly to Podence, whose shot deflected over for a corner.
And from that, Ward was not far from heading the ball into his own net - the ball sailing narrowly past the post.
Nuno's outfit, though, were not exactly in control. A goal to ease the nerves was what was wanted - and they got their wish.
Traore drove through two Palace players - Mitchell and James McArthur - before his low ball found Otto. The Spanish wing-back then expertly shifted it onto his right foot and found the far corner - finishing it like a striker. A big victory, ahead of a gigantic game on Sunday.
Wolves (3-4-3): Patricio; Dendoncker, Coady (c), Boly; Doherty, Moutinho, Neves, Otto; Traore (Neto, 81), Jimenez, Podence (Jota, 71)
Subs not used: Ruddy (gk), Kilman, Saiss, Vinagre, Buur, Jordao, Gibbs-White
Goals: Podence (41), Otto (68)
Palace (4-4-2): Guaita; Ward, Dann (c), Sakho (Kouyate, 22), Mitchell; Townsend, McArthur, McCarthy, Schlupp (Riedewald, 73); Ayew, Zaha
Subs not used: Henderson (gk), Kelly, Woods, Kirby, Meyer, Pierrick, Gordon
Referee: Peter Bankes (Merseyside)