City bossed the first-half pretty much from start to finish with no obvious signs of damaged confidence after the Leicester defeat.
But as ever, it was the masterful Kevin De Bruyne who was pulling the strings as he created chance after chance in the first 45 minutes.
It was all City and finally, with 35 minutes gone, the breakthrough.
City took just four minutes to double that lead and it was Palmer who played a crucial part, winning possession on the halfway line before De Bruyne took over, drove forward and laid the ball to Torres whose clever low cross found Sterling who had time to control the pass and then slot into the bottom right corner.
There were a couple of chances to increase the winning margin, but an excellent performance and a clean sheet was exactly what the doctor ordered.
Torres and Palmer impress
It takes time to adjust to the pace and power of English football but the signs are Ferran Torrres is a quick learner.
Torres' main threat was his variation on crosses with the Burnley defence never quite knowing where he will put the ball.
He capped a fine night with a well-taken goal that will do his confidence no harm whatsoever.
Cole Palmer looked assured and tidy on his debut.
The 18 year-old linked well with De Bruyne and kept things simple and precise throughout.
On another night, the Manchester-born midfielder might have had a couple of goals - but the fact he got in the positions and showed good awareness as he twice came close to setting up Sterling's hat-trick.
What it means…
City move into the Carabao Cup quarter-finals with the draw tomorrow evening on Sky Sports after the Liverpool v Arsenal clash.
How we lined-up:
City travel to Elland Road for the first time in 17 years to face Leeds United in the Premier League (5.30pm kick-off) – the last game before the international break.
You can watch a full-match replay of every City men and women’s first team game within 24-hours of the final whistle on CITY+.