Hull’s formal coronation as the UK’s City of Culture for 2017 takes place on Sunday as the hangovers wear off. On this evidence Robert Snodgrass’s left foot should be among the primary exhibits.

For the threadbare hopes of its football club’s top-flight future appear to hang on the Scotland international’s use of it. Snodgrass has now converted or created exactly half of Hull’s 16 Premier League goals, and for 20 minutes his sixth of the season, an exquisite free-kick, threatened to atone for his compatriot David Marshall’s first-half howler.

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That it did not and that Hull sit one point off the bottom rather than three is down to another recurring theme: an inability to turn good performances into wins. Having handed Ronald Koeman’s team one equaliser on the stroke of half-time, via Marshall’s sliced punch into his own net, they conceded a second to the recalled Ross Barkley’s late header.

Hull, refusing to be deflated by the final 20 minutes of their defeat on the same turf by Manchester City on Boxing Day, started adventurously and took a sixth-minute lead through their second-top scorer, the central defender Michael Dawson. Like Snodgrass’s it was a quality finish.

Neither did Mike Phelan’s team lack spirit. “We are off the bottom of the league,” Phelan enthused. “At times this season things haven’t gone our way but the players are all putting a real shift in. They are listening, learning and have everything to look forward to, which is progress up this league. We have a real battle on our hands in the second half of the season but I think we’re up for it.”

Phelan spoke in the build-up to this contest of the need to reinforce his squad with players “courageous” enough for the fight ahead. Yet it is the grossest of understatements to say that Hull is an even harder sell now than when he did his last recruitment pitch in August on the back of wins from both their opening fixtures.

Nor have his set of summer transfer window purchases proved a raging success. Ryan Mason, the club’s £12.5m record signing from Tottenham, went missing in a relegation duel at Middlesbrough in the first week of December and has not been spotted in a starting XI since; neither has Markus Henriksen, whose permanent £3.5m move from AZ Alkmaar is to be ratified next week; Dieumerci Mbokani has been praised for his hold-up play but is yet to score in 10 appearances since returning to the English top flight.

Two former Manchester United trainees Will Keane and Mike Weir have proved peripheral. The Scotland goalkeeper Marshall, a moderate success, has shipped an average of 2.42 goals a game, and showed himself prone to panicking under pressure soon after Dawson’s finish from a flicked-on Snodgrass corner had put Hull ahead.

Facebook Twitter Pinterest David Marshall punches the ball back into his own net for one of the most bizarre own goals of the season. Photograph: Greig Cowie/BPI/REX/Shutterstock

The sucker punch, quite literally, came in first-half injury time, when Kevin Mirallas swung over a corner and Marshall was cramped by the presence of his own striker Mbokani in his attempt to fist away. The ball skewed backwards for one of the more bizarre Premier League goals of the season. “Everything is fizzing around your head – what you want to say to the players, you know exactly what you want to do and, when that happens with 10 seconds to go, it changes your whole thinking,” said Phelan, of his half-time team talk plans.

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Marshall’s next touch three minutes into the resumption went the same way. Crucially this time, however, his fingertips proved the difference between Romelu Lukaku’s deflected drive hitting the crossbar and flying beneath it.

Then, after Snodgrass found his range by striking the bar in the 55th-minute via a classical up-and-down free-kick – Leighton Baines’s header against the base of a post just shy of the quarter-hour was the first of the attempts against the frame of the goal – he put Hull back in front. One of Harry Maguire’s Beckenbauer-esque marches from deep was crudely halted by Baines, and Snodgrass got the trajectory just right, arcing the ball perfectly into the top corner despite Robles’ attempts to claw it away.

Koeman cited the Yorkshire club’s potency from dead-ball situations – “we knew they’d scored eight out of 14 goals like that,” he said afterwards but conceded that nullifying Snodgrass’ quality was another matter. The same could be said of Hull’s attempts to muzzle Barkley, a player previously dropped as a “wake-up call” by Koeman. Appearing to have been energised by that, and perhaps by the fact Gareth Southgate was among the crowd, he emerged to head in Baines’ dink.

“I hope it gives Ross a boost,” Koeman said. “I think he was the player that we expect in his position. We spoke about him being more dangerous in front of goal, to have better offensive movement and he was really important in the final part of attacking.”