Late Barry leveller lifts City to fourth
City moved on to 45 points from 25 matches, one ahead of Liverpool who have played one game more.
Stoke manager Tony Pulis said his side, reduced to 10-men after 53 minutes when skipper Abdoulaye Faye was sent off, were denied victory by a poor decision from referee Alan Wiley.
Wiley disallowed what would have been a stoppage time winner from Ryan Shawcross, ruling that the defender fouled goalkeeper Shay Given as he headed home from a long Rory Delap throw-in.
"We should have beaten them at the end, the goal at the end was a good goal and its been taken away from us by a poor decision," said Pulis.
"It is pretty poor really, you just hope you get the same as other clubs. You just hope for parity, and we haven't got that tonight."
Faye was shown a straight red card for bringing down Emmanuel Adebayor as the striker collected a long ball from the back.
Despite that blow, Stoke took the lead when City failed to clear after 72 minutes and a mis-hit hoof from Adam Johnson fell to Glenn Whelan 20 metres out whose shot beat the diving Given.
City failed to create a real scoring chance until midfielder Barry scored their equaliser late on.
A long ball into the Stoke box was headed on by Adebayor and after Barry's hooked shot hit a post, his second effort from the rebound beat goalkeeper Thomas Sorensen.
The two sides also drew 1-1 in the fifth round of the FA Cup in Manchester on Saturday and will face each other for the third time in less than two weeks in their Cup replay back at the Britannia Stadium next week.