It says something about the change Roy Hodgson has effected on Crystal Palace that it is difficult to imagine quite how they could be relegated this season.

Make no mistake, Hodgson himself is clear the challenge remains the same as it was when he took over in September and the club was rock bottom, breaking all kinds of the wrong records.

“When I came, I said I was only concerned about the final day of May and being one place above the relegation zone,” he said. But after his scratch Palace side matched Sean Dyche’s Burnley in the gritty part of the game, and won it with the pretty side, their current position of 12th in the table would seem a more likely outcome.

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Bakary Sako scored the only goal of the match midway through the first half, drifting wide to collect Christian Benteke’s looped pass before driving into the box and punching a low shot through Nick Pope. The forward is a symbol of the Hodgson revival, the former Wolves man finally delivering performances that make the best of his combined skill, speed and strength. His total of five goals so far this season is Sako’s best return in his three years in south London, and this was just his second start.

“I don’t know quite how many chances he’s had in the past, but he’s not done well enough to force his way in,” said Hodgson of Sako. “But he’s done really well for us. He would have played today given the injuries we had, but he played on merit and chipped in with a good goal.

“In the second half, he and Benteke worked hard to disturb the centre-halves and help make sure we held on to our lead.”

Palace were without at least seven first-team players for this match. Not only was Sako summoned up front, but James McArthur – “outstanding again”, according to Hodgson – was forced into an unfamiliar position at left wing.

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In midfield, Frank de Boer’s former Ajax protege Jaïro Riedewald also made a rare appearance and applied himself assiduously. There were impressive performances all over the park.

This was particularly the case in the first half. The goal, celebrated with a collective puffing out of the chest, inspired Palace to kick on. A minute after the restart, Charlie Taylor’s back-pass header was seized upon by Wilfried Zaha, who spun it across an open goal, only for Ben Mee to get his body in front of it just in time. Benteke should have scored shortly afterwards from a Luka Milivojevic corner, but his header looped on to the roof of the net.

As the period drew to a close, Zaha forced Pope into a one-handed save with a cheeky flick and the now purring Sako flashed a left-foot volley inches past the far post from Timothy Fosu-Mensah’s cross.

Burnley were better in the second half, upping the combativeness and the crosses without ever quite finding the imagination necessary to unpick Palace’s well-drilled resolve. Their best opportunity arrived in the 83rd minute, when a missed clearance by James Tomkins let in Ashley Barnes, only for Wayne Hennessey to rush out and smother the shot at his feet.

Sean Dyche knows there is no need to be flustered, despite a run that means Burnley are without a league win in six matches. They are still in seventh place in the table after all. “The second half was at least decent,” he said afterwards.

“We probably deserved to scratch a draw. The margins were tight earlier in the season and they continue to be tight now. But it’s clear that we’ve really moved on from last season.”

Dyche was asked about his thoughts on Hodgson’s achievements and the younger Englishman did not hold back in his praise of the 70-year-old. “He’s doing terrific,” he said. “We met for a coffee before the game. We were chewing the fat over the realities and the non-realities of the modern game. Sometimes Roy gets mixed reviews, but the levels he’s worked at, the things he’s achieved, he gets nothing but respect from me.

“He’s settled it down nicely here, but it’s not a surprise to me; it is down to Roy and his staff putting in the work.“