They fell behind in the second minute when Redmond poked the ball into the roof of the net at the near post after James Ward-Prowse released Josh Sims on the right flank and the winger delivered a sharp low cross.
Saints now sit eight points clear of relegation favourites Cardiff, with just five games to play.
"We think it allows us to spend more time together - not just training sessions but social life".
Wolves improved after the break and Jota slashed a shot wide from the penalty spot before Jimenez blazed a volley over the bar from 12 yards out. Rui Patricio returned in goal for Wolves to replace John Ruddy.
Yoshida nearly scored himself shortly afterwards when he was denied at close range by Patricio, and Saints comfortably held out to move a step closer to survival.
- Southampton have won eight of their 18 Premier League games under Hassenhuttl, as many as they had won in 52 games under their two previous permanent managers combined (Mark Hughes 3/22, Mauricio Pellegrino 5/30). It now means that the Saints have won three of their last four league games, and have only lost twice this season at St. Mary's Stadium.
Wily Boly had levelled for Wolves, while Shane Long scored Southampton's all-important third goal.
"The game became harder and the second half was bad".
A number of Southampton players have improved under Hasenhuttl and perhaps chief among those is Redmond.
Southampton return to league action next Saturday, when they travel up to St. James' Park to face Newcastle.
Wolves enjoyed 70% of possession in the game and penned pushed Saints back often, but it was the home side who were much more clinical with the chances they had.