Shwan Jalal saved Jordi Gomez's spot-kick but the Spaniard scored at the second attempt to cancel out Eunan O'Kane's superb first-half strike and earn the Premier League side a fortunate draw.
But the League One team will fancy their chances back on home soil after a spirited display that stretched their unbeaten run to 17 games under returning boss Eddie Howe.
A much-changed Wigan side lined up in their familiar 3-4-3 and proceeded to pass the ball patiently in the early stages without creating any openings for frontrunner Mauro Boselli.
The more purposeful play came from the visitors and there were loud appeals for a penalty when Marc Pugh went down theatrically in the box but he received a caution instead.
Goalmouth incidents were few and far between but the game came to life just before the break as Boselli finally got a shot away that Jalal, picked ahead of David James, saved well.
The Cherries broke quickly down the other end, engineering space for O'Kane on the edge of the Wigan area, and the midfielder let the ball run across him before firing left-footed past Mike Pollitt.
The Latics turned to Manchester United loanee Angelo Henriquez at half-time and the youngster almost had an immediate impact but saw his header from David Jones' free-kick clip the crossbar.
The away side began to sit a little deeper but remained an intermittent threat on the break, as shown when Josh McQuoid curled the ball just over the bar from distance.
Maynor Figueroa then thundered a long-range effort with his trusty left foot that crashed back off the woodwork with Jalal beaten.
But Figueroa did have a role in the equaliser with 20 minutes to play when he was pulled back and referee Robert Madley pointed to the spot.
Gomez saw his tame effort saved by Jalal but was on hand to tuck home the rebound to level the scores and set up an intriguing finale.
But neither side could find a winner so both teams are in the hat for the fourth-round draw and the League One club will have a second chance to cause an upset in the replay.