Gary Bowyer's men had matched their Premier League opponents for much of the first half until, just before the break, Edin Dzeko's flick-on from a corner was headed into the back of the net by Alvaro Negredo.
The home team were gifted an equaliser moments after the restart, though, as Pantilimon spilled Rudy Gestede's header into the path of Scott Dann, who tucked the ball past the Romanian from close-range.
|By Tom Marshall-Bailey
Blackburn Rovers and Manchester City will have to do this all over again at the Etihad Stadium to progress to the next round, with the hosts perhaps the most aggrieved not to be in the hat for the fourth-round draw after a pulsating encounter at Ewood Park.
Manuel Pellegrini's men struggled to get going early on but were rewarded for their persistence right on the stroke of half-time as an offside-looking Alvaro Negredo clinically dispatched Edin Dzeko's flick-on.
But, instead of seizing the initiative at the start of the second half, they were strangely subdued and conceded just 10 minutes after the break as Scott Dann pounced on Costel Pantilimon's shocking fumble from Rudy Gestede's header to level the scores.
Dedryck Boyata was sent off late on to ensure a grandstand finale but City held firm as the first third-round clash of the day ended all square here in East Lancashire.
Pellegrini promised to field a strong side in the competition and he kept to his word, with regulars such as Fernandinho, David Silva and Negredo all handed starting spots, while the Chilean named Joleon Lescott captain after dismissing reports that the defender could leave the club in January.
For the hosts, Paul Robinson made his first start since December 2012 having suffered a blood clot on his lung while Gestede was preferred to leading scorer Rhodes up front.
City, who were defeated in the final of last season's competition, enjoyed plenty of possession in the opening exchanges but were let down by their final ball while Rovers' first effort on target came courtesy of Dann's header, which was easily saved with by Pantilimon.
It sparked the hosts' first spell of pressure as Tom Cairney's free kick delivery and another Dann header caused problems for City's back line.
Silva and Nedgredo both went close midway through the half before City eventually went ahead through the former Sevilla man on the stroke of half time.
Negredo continued his fine form by latching onto Dzeko's header from Silva's set-piece, calmly converting at the far post amid disagreements and shouts of offside from the Blackburn defence.
Blackburn were level 10 minutes after the interval, however, with Pantilimon largely culpable, as he flapped at a routine header from Gestede before allowing skipper Dann in for a simple finish.
City had not lost or conceded a goal in their previous five FA Cup ties against lower division opposition and quickly set about trying to score a second and re-take the lead.
Negredo acrobatically headed wide with an open goal gaping after Robinson saved from Dzeko, before the hosts' goalkeeper was alert to deny substitute Jesus Navas' long-range strike.
City piled on the pressure late in the game but to no avail, and, when Boyata received a second yellow card for a poorly-timed challenge on DJ Campbell, the hosts smelt blood. Cairney went closest with a powerful long-range effort but Bowyer's men had to settle for a replay.