Going into the game, Saints had scored just nine times, while Brighton had just 10 goals from nine matches.
Following the result, Southampton moved up to ninth, while Brighton are now in 11th.
We look at five key talking points from the game.
Van Dijk and Hoedt partnership looks promising
Southampton are one of the best defensive units in the Premier League – it makes up for their lack of goals, and against Brighton, they tried a new centre-half pairing which they hope will be the future for years to come.
That they started together at all would have been a surprise for many in the summer, with Liverpool transfer target van Dijk expected to leave and Hoedt tipped as his replacement.
But Saints insisted they weren’t going to sell their star man and instead he lined up alongside his compatriot.
The Dutch duo showed real potential, too, with van Dijk switching to the right to accommodate Hoedt.
Hoedt’s passing was reminiscent of van Dijk at his best at times – after 14 minutes you could see that when he broke out from the back, to play in Manolo Gabbiadini.
And any questions about whether van Dijk was still committed to Saints were also answered when he held strong as Brighton pushed for an equaliser towards the end of the first half, making two crucial headers, first to clear and then to deny Shane Duffy a certain goal.
That backs up Maya Yoshida’s claims this week that the Dutchman is happy at St Mary’s for now.
“He is good. He is enjoying every day. I think he smiles a lot,” said Yoshida.
“It is very comfortable with him, he never brings any negativity. That's his future, his decision. But, in this moment, he is really comfortable I think.
“It is tough for him but the most important thing is he is with us now and he puts everything on it with Southampton. That is the most important [thing].
“Maybe in the future, something will happen, but at this moment he gives everything to the club. That is very good.”
Southampton may have conceded, but neither of the centre-backs could do anything about Murray’s goal and that bodes very well for the future of the pair indeed.
If van Dijk does stay in January, and there’s no reason Southampton will sell him, there’s real potential for an exciting defensive partnership and that will be good news for both Saints and the floundering Dutch national team.
Do Brighton still need a striker?
Going into the game, Brighton had the second lowest expected goals (xG) in the Premier League – just 6.59.
And scoring goals was clearly an issue for Chris Hughton’s side.
After the summer transfer window closed, the boss himself admitted he wanted to bring in someone else up front but wasn’t able to after, saying: “We can't rely on our No.9s to get us goals.
“I can understand [the negativity about the lack of striker signings] because we did try and it was a position we wanted to bring in and the supporters did as well.
“Once you get to the end of the window it is then the signal to work as hard as you can with the squad you have got. Would we have liked to bring one in? Yes. But we weren't able to and we have to get the best out of the players we have.”
But Murray now has three goals in his last two Premier League games – albeit his only league goals of the season.
He had a quiet first half – his goal was his first shot of the game, but after that, he looked more confident and was great in the air.
With the likes of Pascal Groß putting in some beautiful crosses, Murray may very well be the perfect man for this Brighton side in this 4-4-1-1. Until January at least.
Groß still proving why he’s the bargain of the season
As we hinted above, just how good Groß is isn’t really a secret anymore.
He joined from Ingolstadt for £3million this summer and has shone since then.
Going into the game, he’d been directly involved in two-thirds of Brighton’s goals, with four goals and two assists for the Seagulls’ nine league goals this season.
And once again it was Brighton’s No.13 who was involved in their goal today, playing a lovely cross for Murray to head home.
He nearly was involved in another goal just after, turning Hoedt inside out and playing a ball across the box which the forward fired over.
Nearly every time Brighton looked like scoring, Groß was involved, and there may already be some bigger clubs looking at him, especially his crossing ability.
Saints' style doesn’t suit Gabbiadini
Saints lined up in a 4-2-3-1 which left Gabbiadini very isolated.
They’ve struggled for goals this season, including today’s, they now have nine, but it was hard to blame the Italian for that today, even if he failed to add to his three efforts so far this season.
He only really had one chance, which was a 70th-minute effort blocked well by Duffy.
In the first half, he didn’t even get a shot away and only made six passes – that’s not the statistics of a man who is involved in the game.
He actually only made eight passes all game, as well as attempting just one dribble, which he did complete.
As he fought to get into the game, he completed just three of his nine duels.
With Shane Long now failing to score in 27 appearances for club and country – although he didn’t come on up front today –and Charlie Austin only scoring a penalty so far in the league this season, it’s clear there are striking issues for Southampton.
Saints boss Mauricio Pellegrino will either need to get his striking options more involved in the play or will want to strengthen with someone who better suits what he wants from his forward options.
Boufal fails to take opportunity
Sofiane Boufal called on Pellegrino to start him after coming off the bench to fire Saints to a 1-0 win over West Bromwich Albion last week.
Then he scored a goal of the season contender, running 70 yards before beating Ben Foster.
He celebrated by running up to his manager on the half-way line, before pumping his chest in front of the Argentine, who had been leaving him on the bench.
After the game, Pellegrino was clearly unhappy, saying; “I have spoken with him about that celebration.
“It is obviously something private but the only thing I can say is that I am happy with his action, his reaction on the pitch how he was playing in the last few games and not just the other day.”
But it had an effect, with the Moroccan starting at the Amex, with Pellegrino saying before the game: “Sofiane is a player who is working well.
“In the last three games, he has made an impact in the last 15 or 20 minutes.
“It is not just about his goal – he deserves this opportunity.”
He didn’t take the opportunity though, and after an ineffectual 71 minutes was substituted.
The 24-year-old made just 16 passes, with 66 per cent accuracy, and had just one shot, which was off target.
What’s more, in his four dribble attempts, he only completed one – hardly proving to Pellegrino that he’d been wrong to not start him previously.