For Southampton, this result continues a remarkable turnaround to their season.
Having been relegated in 2024-25 with only 12 points, the second lowest total since the top flight was rebranded as the Premier League in the early 1990s, Southampton were expected to push for an instant return.
When their new boss Will Still was sacked in November, though, Saints were 21st in the Championship and seemingly in danger of dropping into League One.
But the club promoted German coach Eckert from his role with the club's under-21s and they now sit seventh in the Championship, one point behind sixth-placed Wrexham in the final play-off spot.
They face Wrexham in an away league game on Tuesday. The Arsenal game was big, but Wrexham at the Stok Cae Ras could be considered just as important.
Southampton will be at Wembley at least once - in the FA Cup semi-final - and maybe twice more on top if they reach the play-off final and then the FA Cup final.
"It's a big night for us. We knew we had to dig deep in some moments," said Eckert.
"Over the 90 minutes it was very well deserved.
"They're a good team and you can throw problems at them and they always have solutions. They are so well managed and tough to come up against. We had some moments where we did find a couple of solutions.
"Then there are the substitutions that change the game - we made quite good substitutions. In the end it was a big night for us and a big night for the supporters."
Former Southampton defender Francis Benali, speaking on BBC Radio 5 Live, said: "What a result. Just look at what it means to the supporters and the players. I'm proud of them. They deserved it.
"What an achievement against what is a formidable Arsenal side."

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