Christian Benteke took to the field in the 64th minute, coming on in place of Michy Batshuayi as one powerful Belgian frontman for another.
And it was his performance which captain Milivojevic credited with providing Palace an added boost.
He said: "I think Christian Benteke when he came on made the difference in my opinion, especially from the goal kicks: we started to compete in the second half with Christian. From that we tried to create and tried to find some space."
It was from Benteke's pass that Wilfried Zaha earned the penalty which Milivojevic went on to net in now trademark fashion, and the Serbian midfielder offered some insight into how the Eagles' style of play is what wins them so many spot-kicks.
"There is no secret," he said when asked exactly what it is that's led to him netting from 12 yards so unerringly often.
"When one team has as many penalties as we have, that doesn’t come by accident. We have a lot of quality up front, very skilful players. I score a lot of goals which is very important, that you have a player who is constantly scoring the penalties when they happen.
"This season we’ve had a lot, last season we had a lot. We have a lot of pace and skill up front. In the end, I must say I scored the penalty but all credit to Wilfried."
But now, having notched up 39 points, the Eagles can relax somewhat and - with Milivojevic's 28th birthday landing tomorrow - the captain suggested that he and his side can enjoy the next few weeks while looking to rack up further points before ending the season at Selhurst against Bournemouth.
"I think we are safe but it’s not a question of that - you have five games to play, very nice games to play; the next games are City, Arsenal and Everton but let’s say we don’t have that pressure on us at the moment. As well, we must try to get as much as we can from the last five games, especially at home to try to get more points for our fans.
"I forgot it [his birthday] during the game! Tomorrow will be a very nice feeling for me."
To watch more from Milivojevic and his teammates, keep an eye on Palace TV either by clicking here or 'Palace TV' in your official Palace app.