Southampton’s Premier League campaign opened with defeat on the road at Everton, despite Adam Armstrong netting a debut goal for the club.
The striker, who had only arrived earlier in the week from Blackburn Rovers, required just 22 minutes to open his account in red and white stripes, producing a majestic finish to beat Jordan Pickford when clean through on goal to put Saints ahead.
But it didn’t prove enough for the visitors to earn something from the game, as second-half efforts from Richarlison, Abdoulaye Doucouré and Dominic Calvert-Lewin saw Everton take the points.
Hasenhüttl gave debuts to three of his summer signings, as Armstrong, Romain Perraud and Tino Livramento all started, with the latter being handed the first minutes of senior football in his career, following his transfer from Chelsea.
Elsewhere, Alex McCarthy was picked in goal, Jack Stephens partnered Mohammed Salisu at the heart of defence, and James Ward-Prowse was fit to start alongside Oriol Romeu at the base of midfield.
Ahead of them, Moussa Djenepo and Theo Walcott got the nod, with Ché Adams partnering Armstrong in attack.
There was an almighty roar from the Goodison Park crowd as the teams emerged for kick-off, as the long wait for the allowance of full stadiums and away followings finally ended, with supporters also widely applauding as players on both sides took the knee ahead of the whistle.
Into the game, and it was Everton who had the first chance of note, in the third minute, as a Dominic Calvert-Lewin cross from the right was deflected to the edge of the area and into the path of Allan, but his low drive was too close to McCarthy, who made the stop.
Fans from both clubs again joined together in the sixth minute, applauding in honour of Jimmy Gabriel, who had given many fine years to each team, after the sad news of his passing last month.
It was to be a little while then until either side worked a significant opening, but when it came it counted.
Michael Keane was caught dallying on the ball by Adams deep in his own half, and the Saints striker dispossessed him before slipping in Armstrong, who raced towards the edge of the area before opening his body and bending a right-footed shot past Pickford and into the top corner.
It was a magnificent finish and a wonderful way for Saints’ new arrival to cap his debut, as well as a moment to remember for all of the fans who had made the journey for the first away game they had been able to experience in some time.
Having fallen behind, the hosts sought a swift response, but Richarlison was a little too eager in his efforts, falling to the ground in the area as Romeu came to pressure him, with referee Andrew Madley rightly spotting the lack of content and showing the Everton forward a yellow card.
Back at the other end, Armstrong was continuing to prove a nuisance for the home defence, and he was again alert to reach a ball down the left channel and fire in a quick, left-footed snapshot from a tight angle, which Pickford beat away at the near post not long before half-time.
Rafa Benítez, in his first game in charge of Everton, would certainly have had the bigger problems to reflect on at the break, but it didn’t take long after the interval for some of those headaches to disappear, as the hosts quickly equalised.
It came from 47th-minute corner, which, although initially cleared, was headed back goalwards from the edge of the box by Andros Townsend. Salisu appeared to decide to leave it, but as it drifted past him Richarlison was on hand to poke home from inside the six-yard box.
Things were a little edgy for Saints after the goal, although they reached the hour mark without any further damage and ensured the game and the crowd calmed slightly, before beginning to offer a threat themselves again.
But, having appeared to have weathered the storm, they fell behind with a little under 15 minutes remaining.
Doucouré got the goal, bringing the ball under control on the edge of the area, spinning onto his right foot and lashing a shot that clipped the posy on its way into the top corner.
Hasenhüttl responded with a pair of changes, as Nathan Tella and Ibrahima Diallo were sent on for Walcott and Romeu.
But Everton effectively ended the game almost immediately, as Richarlison got onto a ball down the right in the 81st minute and whipped in a brilliant cross that Calvert-Lewin stooped to head past McCarthy.
Saints made their final change as Perraud was withdrawn and Nathan Redmond sent on in his place, but the hosts were able to see it out to the conclusion.