Darren Ferguson’s men put in a strong performance, but were undone by an early goal and a breakaway counter attack strike.
Peterborough United put in a spirited display and dominated possession, but Stoke City took all three points thanks to a deflected strike inside the opening three minutes and a breakaway goal from substitute Tyrese Campbell.
The hosts didn’t take long to open the scoring as former Norwich City man Mario VRANCIC sent a deflected effort from 25-yards into the bottom corner. Dai Cornell was a little fortunate on seven minutes as his clearance struck the back of Brown and rebounded wide of the target.
Danny Batth was cautioned for a late foul in the centre circle on 22 minutes by referee Geoff Eltringham. Jorge Grant curled a free-kick inches over the top on 31 minutes after Szmodics did brilliantly to win a free-kick from Chester.
Grant tried his luck from open play moments later, but his effort looped over the bar via a deflection that the referee failed to spot. Two minutes of added time was indicated by the fourth official, but nothing occurred to report and the half-time whistle was greeted by warm applause from the travelling support, who although disappointed to be behind, would have been heartened by the display.
Jack Taylor was cautioned for a foul on 51 minutes by the referee to give the home side a shooting opportunity from a dead ball situation. Dai Cornell produced two fine saves on 54 minutes, initially keeping out a Fletcher header at the near post before bravely denying Brown by the other post.
Posh were so close to a leveller moments later as Taylor struck the underside of the crossbar, Szmodics headed home the rebound but from an offside position. Stoke made an enforced change on 66 minutes with Morgan Fox replacing the injured Josh Tyman.
Darren Ferguson responded with a change of his own as Jonson Clarke-Harris replaced Norburn in an attacking switch. On 70 minutes, Harrison Burrows replaced Butler at left-wing back. Grant fired wide of the near post on 80 minutes as Stoke made a change in attack with Campbell introduced.
Substitute Josh Knight sliced wide of the near post on 84 minutes with his first touch after coming on to replace Beevers. Stoke were reduced to 10-men as the game moved into stoppage time as Surridge was shown a straight red card for a headbutt into the midriff of Knight, who was cautioned.
Deep into stoppage time, the hosts added a second on the counter attack as substitute CAMPBELL fired home past Cornell.
Stoke City: Davies, Smith, Allen, Chester, Batth, Vrancic, Fletcher (sub Surridge 81min), Tymon (sub Fox 66min), Brown (sub Campbell 77min), Ostigard, Sawyers. Unused subs: Bonham, Wilmot, Duhaney, Ince.
Posh: Cornell, Butler (sub Burrows 70min), Ward, (sub Knight 83min) , Kent, Thompson, Taylor, Norburn (sub Clarke-Harris 67min), Grant, Szmodics, Dembele. Unused subs: Blackmore, Knight, Edwards, Kanu, Coventry.
Half-time: Stoke City 1-0 Peterborough United
Full-time: Stoke City 2-0 Peterborough United
Attendance: 21,285 (1,029 Posh fans)
Referee: Geoff Eltringham