In a lacklustre first half, it was the Cherries who surprisingly took the lead just before the break when Rhoys Wiggins fired home a free kick, from a tight angle following a foul on Marvin Bartley.
After the restart, the Cherries started the brighter, and could have easily extended their advantage, but were denied when a Pugh free kick came back off the woodwork, falling to safety.
The Cherries were left to rue the miss as Lee levelled for the Latics from close range in the 78th minute with Tounkare scoring what proved to be the winner 3 minutes later when he netted from close range.
With the stuffing knocked out of them, the Cherries couldn't manage another effort on goal in the closing few minutes.
The result sees the Cherries slip to 7th, with Carlisle United the visitors to Dean Court next Saturday.
Full report to follow ..................
AFCB: Jalal, Bradbury, Garry, Pearce, Wiggins, Feeney, Bartley, Robinson, Pugh, Cooper, McQuoid
Subs: Stewart, Cummings, Partington, Taylor, Hollands (for Feeney, 77 mins), Fletcher (for Cooper, 82 mins), Arter (for Bartley, 86 mins)