A month on from knocking their opponents out of the EFL Cup, an unchanged Southampton were at their brightest in the early stages when Nathan Redmond got on the ball.
Redmond then drove forward and evaded a couple of challenges before picking out Ings, whose shot deflected wide of Ryan's target.
Minus the playmaking qualities of the injured Pascal Gross, Brighton struggled to create much of anything and soon found themselves behind.
Following near misses for Mohamed Elyounoussi and Ings, the former sending a header wide from eight yards, Hojbjerg showed his teammates how to do it with a long-range bullet.
From a standing start, Hojbjerg sent the ball flying past Ryan into the bottom corner from all of 35 yards out - the first goal Southampton have scored in the opening 45 minutes of a league game this term.
Brighton have never won a game from behind in the Premier League, but the Saints had dropped 11 points from winning positions since Mark Hughes' appointment - a figure that would be added to come full time.
It looked like being the hosts' day, though, with Ings adding a second from the penalty spot after Gaeten Bong caught the Liverpool loanee from behind inside the box.
Brighton were back in the match just 129 seconds later through Duffy's free header from 10 yards - the first time Albion have netted on their travels this term.
The visiting side pressed for an equaliser in the remaining 23 minutes and thought they had it when Alireza Jahanbakhsh clipped the outside of the near post with his flick.
A James Ward-Prowse shove on Duffy when defending a corner led to the referee pointing to the spot for a second time, allowing Murray to send the ball down the middle for his fifth goal in six league starts against the Saints.
SOUTHAMPTON (4-4-2): McCarthy; Cedric, Vestergaard, Hoedt, Bertrand; Redmond, Lemina, Hojbjerg, Elyounoussi (Ward-Prowse 76'); Ings (Davis 84'), Long (Gabbiadini 76')
BRIGHTON & HOVE ALBION (4-4-1-1): Ryan; Montoya, Dunk, Duffy, Bong; Knockaert, Stephens, Propper, March (Jahanbakhsh 71'); Bissouma (Locadia 76'); Murray