Italy went into the game with a 100 per cent record after five games and they appeared to be heading for another victory after an own goal from Shane Duffy and a Ciro Immobile strike guided them to a 2-0 lead.
However, a penalty from the impressive Robbie Brady in the 61st minute was followed five minutes later by an equaliser from Greg Cunningham.
Italy's miserable second half was rounded off when Marco Verratti was given a straight red card in injury time for tripping Aidan White.
The draw sees the Republic move to within two points of second-placed Turkey, with Noel King's men having two games in hand.
It also means the Republic are unbeaten at the Showgrounds in these qualifiers, but that record was under threat after the hosts made the worst possible start as Duffy sliced Alessandro Flore's curl free-kick into his own net in only the third minute.
The visitors were putting the Republic defence under severe pressure. Mattia Destro was played in but a less-than-perfect touch allowed goalkeeper Ian McLoughlin to smother the ball while Immobile squandered a glorious chance.
The hosts started to inch their way into the match, Eunan O'Kane sending a shot wide from distance.
Good interplay from O'Kane and Murphy looked promising but the former's ball from the left was poor and any chance had gone with Duffy putting a header straight into keeper Francesco Bardi's arms from close range as the Italians ended the first half untroubled.
Jeff Hendrick burst into the box but was dispossessed by Alessandro Crescenzi and moments later Destro drilled a shot from 25 yards which went just wide of McLoughlin's post with the keeper stranded.
However, the Italians extended their lead 11 minutes into the second half, Immobile dribbling along the edge of the area before turning and shooting into the corner of the net.
The Republic's task got harder when O'Loughlin was replaced by Aaron McCarey because of injury but against the odds they pulled a goal back in the 66th minute from the spot.
Destro handled in the area and Brady hit the ball into the bottom right-hand corner with the keeper going the wrong way.
McCarey saved from Destro but the Republic drew level in the 71st minute and again Brady was involved.
His free-kick from the right found Cunningham whose header, although weak, trickled into the corner of the net, although there was some confusion it may be an own goal.
There were no further openings for either side, but Italy's disappointment was compounded when Verratti was given a straight red card in injury time.