“Shall we score a goal for you?” the home fans chanted, and well they might, with Pep Guardiola’s side having now scored 16 goals in three Premier League games.
By contrast, Palace are still yet to score in the league and have now lost six games in succession.
Sane and Raheem Sterling, who scored twice, did the damage, while Sergio Aguero and Fabian Delph added gloss to the scoreline at the Etihad Stadium.
The win keeps City on top of the table, edging in front of rivals Manchester United on goal difference.
It was frustrating for City until they were able to edge in front just before the break.
Palace defender Mamadou Sakho flicked Kevin De Bruyne’s cross onto his own post and Sane fired over after skipping through several challenges.
But for all of City’s early possession, it was Palace who had the better chances in the opening stages.
The south London side, playing under Roy Hodgson for the second time in the league, looked well drilled and could have stung the hosts on the break.
Ruben Loftus-Cheek had an effort deflect off Nicolas Otamendi and onto the post, having beaten England centre-back John Stones twice to get into a shooting position on 19 minutes.
Loftus-Cheek went close again, sliding a shot wide when it seemed easier to score after Timothy Fosu-Mensah’s low cross nicked off Fernandinho.
City’s disjointed start to game was not helped as the home side lost Benjamin Mendy to injury mid-way through the first half.
The France left-back clashed knees with Andros Townsend, giving away a tactical foul as the winger skipped past, and was replaced by Danilo.
– Aguero closes on Brook –
City had to work to forge chances, but the pressure was eased on the stroke of half-time.
Quick interplay between Sane, De Bruyne and David Silva allowed the Spaniard to lift a pass to Sane on the left.
He flicked it over the head of Scott Dann and slid a shot through the legs of Wayne Hennessey.
The goal opened the visitors up. Six minutes into the second half, a quick break saw City double their lead.
Again Sane was key. His break down the left flank was picked out by De Bruyne and a perfect low cross into the path of Sterling meant the England winger could not miss.
Presented with what seemed an even easier opportunity a minute later after Hennessey’s touch on De Bruyne’s cross presented him with an open goal, Sterling side-footed wide.
Aguero was now on the hunt for the goals to take the club’s scoring record.
Having found space on the edge of the box, he skipped past three challenges to go one-on-one, but fired his left-foot strike straight at Hennessey.
It was one-way traffic. Sterling doubled his tally and took City’s to three after De Bruyne’s ball to the back post was touched into the winger’s path as he arrived late into the six-yard box.
All eyes were now on Aguero, who began the day needing two goals to join Eric Brook as City’s all-time leading scorer.
The Argentina striker netted with 11 minutes to play, heading in Sane’s searching cross to close to within one goal of Brook’s haul of 177 goals.
Palace were begging for full-time by the time Fabian Delph made it 5-0, the substitute curling a sublime effort into the top corner with his weaker right foot.