Call off the search. After two wins in the space of a week, Craig Shakespeare can head to Dubai with the Leicester City players for their warm weather training camp fully expecting to be given the news that he will remain in charge for the remainder of the season. Claudio Ranieri’s former assistant has done everything that has been asked of him and more and it would be a strange decision to look elsewhere now that Leicester have remembered how to win football matches.

Vichai Srivaddhanaprabha, the chairman, and Aiyawatt, his son and vice-chairman, were in the directors’ box on a day when Leicester played with spirit and belief to record back-to-back Premier League wins for the first time this season. It was also the first time in this campaign that Leicester have won a match after falling behind. The turnaround was indicative of the newfound confidence and resilience in a group of players who appear liberated.

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Riyad Mahrez is a case in point. The Algerian produced a moment of brilliance here to score his first league goal from open play since April. Christian Fuchs, another who had toiled under Ranieri, had equalised for Leicester and any hopes Hull had of salvaging something from this game were extinguished when Tom Huddlestone headed into his own net in the 90th minute, leaving Marco Silva’s side second bottom and four points adrift of a safe position.

Leicester’s transformation since Ranieri’s dismissal may sit uncomfortably with some, yet the fact is that the Italian had got things wrong this season with his tactics and his team selections. Shakespeare has gone back to the Leicester of old, with Shinji Okazaki restored to the starting lineup and the players encouraged to press aggressively high up the pitch.

The rewards have been there for all to see. In the bottom three before the victory over Liverpool on Monday night, Leicester are now five points clear of the relegation zone and the optimism around the club is almost tangible. The game finished with the home supporters singing Shakespeare’s name, big smiles in the directors’ box and huge cheers greeting the final whistle.

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For Leicester’s owners there must be a sense of vindication as well as relief, with the club now under no pressure to pursue Roy Hodgson or any of the other candidates they had spoken to in the wake of sacking Ranieri. Shakespeare has the backing of the fans as well as the players and it would be a risky policy to bring in someone else and risk disrupting the feelgood factor that has returned.

Not that Shakespeare is going to start shouting from the rooftops about his prospects. The 53-year-old answered questions with the straightest of bats after his latest success. “I was told the remit was the Liverpool game and then Hull,” he said. “I’ve been told now – and I’m quite comfortable with it – that we’ll have a talk towards the end of the week. I’m more pleased about the results than anything else.”

Hull, in contrast, are in deep trouble. Although they took the lead through Sam Clucas, who started and finished a counterattack that stemmed from Wilfred Ndidi giving the ball away deep inside the Leicester half, that came against the run of play and the visitors looked vulnerable defensively throughout. A gap has now opened up at the bottom and next Saturday’s home match against Swansea appears critical in terms of their survival prospects. “The numbers are not good for us, that is clear,” Silva said.

Facebook Twitter Pinterest Hull City’s Tom Huddlestone reacts after his own goal secured victory for Leicester. Photograph: Steven Paston/PA

Leicester’s equaliser arrived shortly before the half-hour mark, following a lovely move down the left flank involving Fuchs and Jamie Vardy. The pair swapped passes a couple of times before Vardy darted into the area and cut the ball back for Fuchs, who hit a right-foot shot from 10 yards that seemed to go through the Hull goalkeeper, Eldin Jakupovic.

Harry Maguire had two good chances to restore Hull’s lead shortly after the restart, his first effort hitting the outside of a post and the second saved by Kasper Schmeichel. That was the cue for Mahrez to take centre stage. Twisting and turning on the edge of the Hull area, Mahrez showed some lovely footwork to leave Andrew Robertson totally disorientated. Having created a yard of space with a neat Cruyff turn, Mahrez drilled a 20-yard shot that flashed inside Jakupovic’s near post.

Oumar Niasse forced Schmeichel into a decent save late on but Huddlestone’s own goal moments later put the outcome beyond doubt and allowed Leicester to celebrate a rare comeback win. “I’ve just reminded the players of that,” Shakespeare said. “To go 1-0 down in the manner we did, on a counterattack … we showed great character and resilience to bounce back.”