Lazio produced a stunning fightback after goals from Enzo Maresca and Nicola Caccia within the first half hour put Piacenza in the ascendency.
But Lazio were level before half-time courtesy of goals from Argentine duo Diego Simeone and Claudio Lopez.
Just as it appeared Lazio would have to settle for a point, Corradi pounced two minutes into stoppage time.
Milan relinquished top spot after a 1-1 draw at Empoli, who cement their position in mid-table.
Tommaso Rocchi fired the hosts ahead just before the break but Andrei Shevchenko continued his fine form with the leveller on 52 minutes.
Internazionale join their city rivals on 26 points after a crushing 4-0 success over hapless Brescia.
Italian international Christian Vieri grabbed all four goals, with a brace in each half to leave Inter on the heels of leaders Lazio.
Juventus missed an opportunity to go back to the top of Serie A after coming from two goals down to earn a 2-2 draw with Roma in the Stadio Olimpico.
The home side started brilliantly as Francesco Totti gave Roma a 1-0 lead after just 12 minutes.
Antonio Cassano doubled their advantage with a minute remaining in the opening half as Roma looked certain to go into the break two goals up.
However a minute later, Juve received a lifeline when Alessandro Del Piero pulled it back to 2-1 just before the half-time whistle.
The second period saw the Roman club seemingly heading towards a key victory but with five minutes remaining, Czech Republic star Pavel Nedved pounced to score a crucial equaliser for the Turin giants.
The final two minutes of the match saw plenty of fireworks as three players were sent off before the end.
With two minutes left, Roma's Frenchman Vincent Candela and Juve's Alessandro Birindelli were both shown red cards.
Then in the last minute, the home side were reduced to nine men as Totti was also dismissed by the match referee.
The result leaves Juve fourth in the table and level on points with Milan and Internazionale while Roma sit in ninth position.
Bologna remain within hailing distance of the top after a 3-0 home win over Modena.
Tomas Locatelli's 56th minute goal broke the deadlock and strikes in the closing ten minutes from Julio Cruz and Christian Amoroso sealed the points.
Parma compounded Torino's current woes with a thumping 4-0 triumph at Stadio Delle Alpi.
Matteo Brighi and Adrian Mutu scored in the first half and a second half double from Adriano added gloss to the score-line.
Perugia picked up a comfortable 2-0 win at Atalanta despite finishing the match with ten men.
Fabrizio Miccoli scored on 20 minutes and Massimiliano Fusani effectively settled matters with ten minutes to go before Chris Obodo was dismissed in injury-time.
Click below for an individual match summary:
Serie A
Atalanta 0-2 Perugia
Bologna 3-0 Modena
Empoli 1-1 Milan
Internazionale 4-0 Brescia
Piacenza 2-3 Lazio
Roma 2-2 Juventus
Torino 0-4 Parma
Click here for an updated Serie A table.
