At half-time, Millwall’s supporters must have been convinced this was going to be their day. Leading in the south London derby thanks to a howler from the Crystal Palace goalkeeper, Jack Butland, a famous FA Cup upset seemed very much on the cards.

Unfortunately for them and their manager Gary Rowett, Michael Olise had different ideas. A sparkling 13-minute period at the start of the second half during which he equalised, hit the post and then set up Jean-Philippe Mateta for what proved to be the winning goal was more evidence of the 20-year-old’s burgeoning talent.

Related: Millwall 1-2 Crystal Palace: FA Cup third round – live!

“He was fantastic in the second half,” said Palace’s manager Patrick Vieira. “He changed the game for us but it was like watching two different players in the first and second half. We know how good he can be so it’s about trying to help him reach that level of consistency.”

Apart from reaching the quarter-finals under Roy Hodgson in 2019, Palace’s record in this competition has been awful since they came within nine minutes of beating Manchester United in the 2016 final, having been eliminated in the third round for the past two seasons. With that in mind, Vieira fulfilled his promise to select a strong side that included Conor Gallagher on his return from injury.

Since Palace’s last trip to the Den nearly nine years ago, Millwall have flirted with the top half of the Championship table but not quite managed to reach the play-offs despite a couple of close things. Their chances of reaching the top flight for the first time since 1990 were not helped by a run of three defeats in their last five league matches and this was a welcome opportunity to make a statement against their more illustrious neighbours.

While neither club would describe the other as mortal enemies, there is certainly no love lost between teams separated by just six miles, and there was an intense atmosphere at kick-off. Palace fans in the away end set off flares and there was widespread booing from all sections of the home support of those players who took the knee. Homophobic chants were also aimed at Gallagher and are likely to be punished, while Olise was struck by a bottle as he prepared to take a corner in the second half.

Rowett remembered this week how he had been on the end of some real beatings against Vieira’s Arsenal during his playing days with Derby, but his side clearly had a gameplan from the start here and they sprang out of the traps. Millwall should have gone ahead in the eighth minute when Benik Afobe blasted wide from close range but the former Arsenal striker would be handed another opportunity on a plate soon after.

Quite what Butland was contemplating when he decided to take an extra touch under pressure from Tom Bradshaw only the goalkeeper will know, and Afobe was a grateful recipient of his weak clearance. Had George Saville made the most of a subsequent chance inside the penalty area then it could have been much worse for the visitors. While Eberechi Eze – making his first start since returning from a lengthy injury layoff – started to grow into the game against his former club after Palace’s lacklustre start, it was Vieira who headed down the tunnel feeling frustrated after Saville’s well-timed challenge on the Palace midfielder inside the area went unpunished.

Whatever he said during the break clearly had the desired effect. Barely 40 seconds of the second half had elapsed when Gallagher picked out Olise on the right and he unleashed a brilliant curling shot that went in off the far post. The 20-year-old was then inches away from doubling his tally and putting Palace in front six minutes later with a carbon copy, only for the ball to bounce off the post and away to safety this time.

The loss of the influential Saville to injury suddenly left Millwall struggling to hang on and Olise again went close. But they could do nothing to stop him turning provider for Mateta as an inch-perfect cross picked out the unmarked Frenchman to complete the turnaround. Mateta’s celebrated in front of the home fans and was pelted with plastic bottles. Several flares were also set off by the Palace fans, causing a delayed restart. “We conceded two poor goals from our point of view,” said a disappointed Rowett.

The Millwall manager abandoned his three-man defence and threw on Mason Bennett in a bid to find a way back into the tie. Substitute Matt Smith’s header in added time was their big chance, but this time Butland was solid.