A dominant display, which saw Kompany fire a superb second-half strike, lifted Pep Guardiola’s side up above Liverpool into third place in the Premier League table on goal difference.
In what was a sublime all-round performance, David Silva netted his 50th goal for City to open the scoring after just two minutes.
Kompany then drilled home a superb strike early in the second half before Belgian colleague Kevin De Bruyne, Raheem Sterling and Nicolas Otamendi rounded things off in the day’s early kick-off.
With home games to come against Leicester and West Brom before the season’s finale away at Watford, it means City are in control of their Champions League destiny – and Kompany is urging his side to repeat the approach that paid rich dividends against Palace for the remainder of the campaign.
“We wanted to set this chain of home games right and it couldn’t have gone any better,” said the centre-half.
“We need to repeat the performance in the next two game at home.
“If we do that it should put us in a great position going into the final league game away at Watford.”
It was Kompany’s first goal at the Etihad since 2015 and one of his most spectacular strikes in a Blue shirt.
But though spectacular, the captain said it still didn’t rank as his best goal for the Club.
“It depends if you talk about emotions. The one against Man United (in April 2012) will always be best,” Kompany added.
“It was only 1-0 after the first half so it wasn’t an easy. We kept shooting and kept trying and we forced it to go our way. We needed that.”