Southampton had everything to play for, Arsenal had nothing to play for, and yet despite the unbalanced motivations these two produced a back-and-forth classic at the Emirates this afternoon.

Mark Hughes’ Saints, desperate to drag themselves out of the relegation zone, took the lead, let it slip, fought back but lost the game at the end. They finished disconsolate, defeated again and three points adrift of Crystal Palace with just six games left. But this was a world away from the 3-0 defeat at West Ham United last weekend. This time they even looked like they wanted to stay up. Which is a start.

For Arsenal the motivation was less clear. Like Manchester United did last year, they have re-allocated all their eggs to the Europa League basket, which means they have to hold off CSKA Moscow in Russia on Thursday night. So Arsene Wenger made seven changes here, resting Mesut Ozil and Aaron Ramsey, and requiring a different type of goal threat. Less creativity, more cutting edge. So he paired Danny Welbeck with Pierre Emerick Aubameyang up front, surely the fastest front pair seen in the Premier League this season.

All these changes meant that this Arsenal team had to feel their way into the game, had to remind themselves of its importance compared to their European adventure. For Southampton the stakes were very clear from the start: Crystal Palace and Huddersfield Town drawing yesterday at least gave them something to aim at, some heels to grab onto as they try to pull themselves out of the relegation trench.

Southampton started like they knew that. Even in this new 5-4-1 formation, Saints could get bodies forward and cause some problems. Arsenal did not exactly make it difficult for them either. When Calum Chambers skewed a clearance, Dusan Tadic found James Ward-Prowse, and Hector Bellerin had to scramble back to the line to clear the ball. Soon enough they took the lead, thanks to Arsenal defending even worse than for Charlie Austin’s late equaliser. Sead Kolasinac allowed Ward-Prowse to cross from the right, Shkodran Mustafi stood still as Shane Long darted in front of him at the near post to turn the ball past Petr Cech. Even in Mustafi’s error-riddled season, this was a bad one.

But even with the lead, and with their new system, this Saints team never felt secure. How could they when their defensive record is so bad and they have brought in Hughes, more aggressor than organiser, to fix it? Once Arsenal started playing they found their way through, and two goals in 10 minutes put them ahead at the break.

The first good combination of the new front two saw Welbeck take Iwobi’s pass and flick it into the path of Aubameyang, under pressure, bearing down on goal, but just able to touch the ball past Alex McCarthy in goal. With Arsenal’s next attack, Welbeck showed another side to his game, all power and audacity. Cutting in from the left, surging away from Stephens and Ward-Prowse, his shot looped off Maya Yoshida’s heel and flew in.

Arsenal are not quite as loose with a lead as Saints, but they are not much better. Missing chances to go 3-1 up early in the second half, they started to let their visitors back into the game. And when Hughes sensed the moment and threw on Charlie Austin, Saints were level again within seconds. It took more passive Arsenal defending to wave them through: Cedric exchanged passes with Tadic and ran into the box, Chambers stood and watched, Austin turned in the cross unchallenged.

That was 2-2 and Southampton had 17 minutes to find an unlikely winner, a goal to change their whole season. But the more men they threw forward, the more space they left at the back. And Arsenal had the quality to exploit it. First Iwobi crossed to Jack Wilshere, who set up Welbeck, who missed an open goal. But the next time they made no mistake: Iwobi outmuscled Tadic, stood the ball up to the far post, where Welbeck leaped above Cedric to head in.

Welbeck’s second goal was Arsenal’s third, and this time there was no Southampton comeback. They had nothing left in the tank and Cech only had one simple save to make from Tadic at the end. Saints’ last hopes were extinguished when Jack Stephens was sent off for shoving Wilshere to the floor after having his shirt ripped into two by him. In the ensuing scuffles Mohamed Elneny was sent off too. Not that Arsenal will mind: their focus is on Europe after all.