Southampton defender Jannick Vestergaard scuffed his attempt to give the ball back to goalkeeper Alex McCarthy before Paterson gained possession and scored his fourth goal of the season in the driving rain.
The victory was the third in a row at home for Cardiff, which had not won three straight top-flight games at home since 1961. It was also its first clean sheet since late August, with goalkeeper Neil Etheridge having been challenged just once.
Hasenhuttl, appointed to replace Mark Hughes earlier in the week, left Bundesliga team Leipzig in May. He immediately made his presence felt with six changes from the team that lost to Tottenham on Wednesday, but they weren't enough as Southampton extended its winless run to 14 games.
More AP English soccer: https://apnews.com/tag/PremierLeague and https://twitter.com/AP_Sports