The England Under-21 international struck just before the hour mark after Shane Long had been fouled in the area by Alex Bruce.
Pelle then struck his first league goal of 2015 as the Saints recorded a comfortable victory that lifted them up to fifth, while the result sees Hull teetering precariously in 17th place in the table, just above the relegation zone.
Southampton had a great chance within seconds of kick-off through Long who found himself clean through inside the first minute but stumbled over his first touch and failed to test Steve Harper in the Hull goal.
The Tigers were soon on top, though, and Sone Aluko had two chances to put his side ahead – first an effort he scuffed wide when presented with the ball just inside the Saints area, and second when he fired straight at Kevin Davis after carving himself out a decent opening.
But it was Pelle who spurned the best chance just before the midway point in the half. Long managed to win possession in the area before the ball found its way to his Italian strike partner. Six yards out, however, he could only hit Harper – who reacted impressively to close down the angles.
The game gathered pace as the half went on and Southampton started to dominate, especially in the middle of the park where the excellent Morgan Schneiderlin pulled the strings alongside Victor Wanyama – who managed to pick up his 10th booking of the season, which will see him ruled out for the next two games.
Saints continued to boss the game after the break and just before the hour mark they were in front, Ward-Prowse converting his penalty superbly past Harper after Long had been needlessly fouled by Bruce after bursting into the area.
Harper was only in goal because Hull boss Steve Bruce decided to drop Allan McGregor – who had saved the last three Premier League penalties he had faced and was on the bench.
Southampton continued to dominate and, with just less than 10 minutes left on the clock, they put the game beyond Hull through Pelle – who struck from close range after some excellent work from Schneiderlin.
Steven Davis could have made it three late on, but for Southampton it was three well deserved points that saw them equal their total from the whole of last season.
SOCCER SATURDAY VERDICT – Alan McInally
“Steve Bruce says Pelle should have been sent off but I don’t agree. He hits Bruce with his left arm square in the mouth but I genuinely think it was unintentional. A yellow card was maximum. He would have been very unlucky to be sent off.
“It was a difficult day for Alex Bruce. He took a couple of bangs in the face but – and I agree with Steve on this one – he can’t make the challenge on Long. In the first half Hull were pretty good. Livermore brought a brilliant save out of Davies, Aluko has a chance, Quinn with a volley, Chester has one headed off the line… they hadn’t played that badly. But the penalty changes everything on 56 minutes.
“Hull had genuine opportunities to score. I feel for them. But Southampton didn’t play that fantastic.”
Southampton: K. Davis (7), Alderweireld (7), Fonte (7), Yoshida (7) Bertrand (7), Wanyama (6), Schneiderlin (8), S. Davis (6), Mane (6), Long (7), Pelle (7)
Subs: Ward-Prowse (7), Tadic (6), Elia
Hull: Harper (6), Chester (5), Dawson (5), Bruce (4), McShane (5), Elmohamady (6), Livermore (5), Huddlestone (5), Quinn (5), Aluko (6), N’Doye (5)
Subs: Diame (5), Sagbo, Hernandez
Man of the match: Morgan Schneiderlin