The Potters made just one change to their starting line-up as Tchamadeu returned at right-back in place of Maksym Talovierov, and it proved to be an inspired decision.
The Cameroon defender got past Neto Borges and fired in a powerful low cross that Manchester City loanee Mubama fired in from six yards.
The Robins responded well to going behind as they forced a number of corner kicks. George Tanner’s decent effort was deflected wide, while Rob Dickie went close with a header.
But Mubama continued to impress as he glanced a 19th-minute header over the bar before getting his second in fortuitous circumstances. Manhoef’s overhit pass seemed to be routinely gathered by Vitek, but the ball hit his knee as he slid to claim it and squirmed to the feet of Mubama who rolled it into the empty net.
Three minutes later he turned provider as Manhoef cut in from the right and exchanged passes with Mubama on the edge of the box before arching a left-footed strike into the bottom corner.
To the Robins’ credit they did not buckle as Anis Mehmeti’s low shot forced a good save from Viktor Johansson, while Sykes had an effort deflected over.
But any hopes they had that they might get back into the game were snuffed out almost as soon as the second half kicked off.
First Stoke thought they should have had a penalty kick when Lewis Baker appeared to be fouled by Rob Atkinson, but after the ball was cleared, Tchamadeu galloped down the right wing, beat two men and fired low into the bottom corner.
The visitors did not give up – Mehmeti, Ross McCrorie and Sinclair Armstrong had chances after the fourth goal – but Stoke never looked in any danger.
They got a fifth goal when Lamine Cisse put Mubama through and the 21-year-old powerfully found the net from 12 yards, while Sorba Thomas saw his effort to get a sixth palmed away soon after.
But Sykes got a consolation goal that Bristol City’s attacking efforts more than deserved when he flicked on Yu Hirakawa’s corner kick at the near post and it looped into the net.