City manager Pep Guardiola welcomed captain Vincent Kompany back into his side for the first time since November, when he suffered knee ligament damage at the same ground, and the Belgium centre-back was rarely extended by Sam Allardyce's men over the course of 90 minutes.
Palace's best spell of pressure immediately preceded the opening goal, when Sterling gratefully accepted and converted a beautifully judged pass from full debutant Gabriel Jesus two minutes before half-time.
Sane was a big-money arrival from Schalke during the close-season and, having taken time to settle in England, the 21-year-old Germany winger made it three goals in as many appearances when David Silva pulled Palace apart in the 71st minute.
Toure made his surprise return to the City starting line-up at Selhurst Park two months ago and, now part of the furniture once more, he garnished victory with an excellent free-kick in stoppage time.
Overall, City rediscovered the clinical edge Guardiola has criticised them for lacking too often this season, although Sane made an inauspicious start with a dreadful headed miss from Sterling's third-minute cross.
Fabian Delph, like Kompany back in the side following a lengthy injury absence, was the next City player to botch a header from a dangerous Sterling delivery.
Referee Mike Jones drew the ire of the home supporters with half an hour played when, having booked Toure two minutes earlier, he neglected to produce red after the former Ivory Coast international fouled Jordon Mutch.
Palace striker Christian Benteke headed over from the resulting set-piece before City goalkeeper Willy Caballero was called into action, plunging to his left to superbly deny James Tomkins at close quarters.
The visitors appeared to be the side most in need of half-time but hit the front when Sterling latched on to Jesus' throughball and relocated his early season poise to slot past Wayne Hennessey.
The Wales keeper reacted brilliantly to deny Jesus what would have been a crushing second on the stroke of the interval.
Allardyce introduced Loic Remy in place of Benteke as his attacking spearhead at the break and the Frenchman quickly made a nuisance of himself, harrying City centre-backs Kompany and Aleksandar Kolarov before thrashing a 50th-minute volley over.
Guardiola's men responded, with Sterling attempting a backheel finish following probing work from Sane and Hennessey tipping Delph's drive from the edge of the box wide.
Joe Ledley whistled a strike narrowly wide after the hour, as torrential rainfall became heavy hailstones – a brief interlude of extreme weather that had passed by the time the tie was settled.
Silva strode purposely towards the heart of the Palace defence, masterfully orchestrating a counter-attack that reached its crescendo when the Spain playmaker picked out Sane for a calm finish.
Ledley headed beyond the top corner as the clock ticked down but he was notably short of willing allies as the Eagles slumped to a fifth defeat in eight outings under Allardyce.
The Wales midfielder's last notable involvement was one to forget as he brought down the relentless Jesus for Toure to add the final flourish from 30 yards.