Samuel Eto'o struck from close range to give the champions an early lead and after the hosts missed a succession of chances in the second half Caracciolo finally equalised five minutes from time.
The same player then missed a penalty in the 90th minute before being sent off in stoppage-time. Inter's Ivan Cordoba had also been dismissed in the closing stages.
Brescia goalkeeper Michele Arcari was powerless in the 18th minute when Eto'o latched on to Andrea Ranocchia's flick to volley his 19th league goal of the campaign.
Caracciolo, who headed weakly at Inter keeper Julio Cesar earlier, wasted a good chance to level on 35 minutes when he lobbed the ball high over the bar.
With the impressive Wesley Sneijder pulling the strings in midfield, Inter started to dominate.
The Dutchman struck the post from 25 metres on 55 minutes and then fired straight at Arcari.
The Brescia keeper came to the rescue again soon after to deny Goran Pandev.
With Tuesday's Champions League last-16 return match against Bayern Munich in mind, Inter coach Leonardo brought on Cordoba for Lucio with 25 minutes to go but the move backfired.
Colombian defender Cordoba misdirected a header to allow Caracciolo to score and then received his marching orders for upending Brazilian Eder in the penalty box.
Caracciolo's spot-kick was saved by Julio Cesar before the Brescia striker completed an eventful evening when he was shown a second yellow card deep into injury-time.
