Southampton were denied a huge step towards Premier League survival when Everton prevented a second successive league victory under Mark Hughes through a last-gasp equaliser from Tom Davies. The visitors must have thought they had done enough to win, with Nathan Redmond even bringing a late save from Jordan Pickford when Southampton had been reduced to 10 men, but when Ryan Bertrand gave the ball away with just seconds remaining Davies crashed in a shot from Idrissa Gueye’s square ball via a deflection off Wesley Hoedt.

The only consolation for Southampton is that they still managed to move out of the bottom three and above Swansea, going into the all-important meeting in South Wales on Tuesday. There was also another reprieve for West Brom, who would have been relegated by a Southampton victory, but little respite for Sam Allardyce. Though Everton have been safe for some time their manager’s position is looking increasingly precarious. Allardyce was hoping to use this game to leave Everton fans feeling positive over the summer, and it is doubtful whether Davies’s late rescue act will have quite that effect.

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Hughes was furious at the end because Jon Moss awarded a free-kick against Redmond for an offence no one else had seen, then allowed Everton to take it from the wrong place. Not what you need when you are shorthanded and trying to cling on for dear life. “Jon Moss was 30 yards behind the play, as he usually is,” the Southampton manager said. “He gave a free-kick that shouldn’t have been. At least we took something from the game. Everton had to change their shape to match us and we were still better at it than they were. We got everything right in the game until the final few moments, and we didn’t get any help from the officials.”

Davies showed willing in the opening minutes with a shot from the edge of the area that was not too far off the target, though Everton failed to keep up anything like the same urgency. Cenk Tosun headed over the bar with a difficult chance from a Séamus Coleman cross but that was about it for home attempts on goal in the first half and Allardyce was soon in his technical area gesturing furiously for his side to get men further forward.

Southampton were the first side to bring a save from a goalkeeper, and a very good one it was too from Pickford, whose reactions did not let him down when Charlie Austin sent in a volley on target with little warning after the ball came his way off Michael Keane. By the half-hour mark Southampton were looking the more likely to make a breakthrough and Everton were glad Phil Jagielka was in the right position to make a timely interception when the ball came through to Oriol Romeu in front of goal.

To say the game was low on incident and excitement would be a considerable understatement. The home side departed to boos at half-time, though that has become par for the course in recent weeks. Even when Everton won at Huddersfield last week there was still dissatisfaction expressed at the style of football being played under Allardyce. Or perhaps just the continued presence of Allardyce. The school of science, it is being said by some unhappy supporters, is presently in special measures.

Allardyce is impervious to that sort of background noise, of course, and as a half-time flourish to mark the end of his first season at Goodison he brought on Ramiro Funes Mori for Yannick Bolasie and switched to a back three. He does not exactly court popularity, though something needed to change and after an anonymous first half the winger could hardly complain.

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Southampton also made a change, Redmond replacing the ineffective Mario Lemina, and 10 minutes after the restart it was Hughes looking smug on the sideline. Dusan Tadic and Cédric Soares found space on the Everton left behind the now advanced Leighton Baines – always the drawback with wing-backs – and from the latter’s precise cross Redmond arrived in the area to beat Pickford with a firm downward header. Cue joy in the small corner of the Bullens Road stand that was red and white and more boos from the blue majority.

The visitors were forced to see out the last five minutes with 10 men after Maya Yoshida picked up a second yellow for a foul on Oumar Niasse. Baines brought a brilliant fingertip save from Alex McCarthy with a stoppage-time free-kick but time was running out when Bertrand made his mistake and invited Everton to claim a point they barely merited. That may sound harsh but Allardyce himself admitted it. “We nicked a point we didn’t deserve,” the Everton manager said. “It’s disappointing but we have made overall progress.”