The most successful part of Tafi's career was spent with the Italian super-squad
Mapei–CLAS. In the 1996 edition of Paris–Roubaix the team put four of their riders in a breakaway at the front of the race:
Gianluca Bortolami, previous year's winner
Franco Ballerini, and Tafi. Ballerini had a flat and was out of the lead group, but the other three powered their way to the finish.
In 1996 Tafi won the "race of the falling leaves"
Giro di Lombardia, using his strength to overcome the climbs of the race. He said that his dream was to emulate his cycling hero fellow Italian
Francesco Moser, which is to win Paris–Roubaix wearing the Tricolore jersey as the Italian National Champion. He accomplished this in his win in 1999.
 He won
Paris–Tours in a long breakaway effort in 2000, foiling the
sprinters' teams. After a few lacklustre years, he again shone in the 2002 edition of the hilly, cobbled classic Tour of Flanders. Having established himself in a front breakaway with the likes of Johan Museeuw,
Peter van Petegem and teammate
Daniele Nardello, he made attacks after attacks, finally taking advantage of a moment's hesitation between the two home favorites Museeuw and van Petegem to solo to the finish for the win.
After the demise of the Mapei super-team, Tafi moved to the reformed
Team CSC under
Bjarne Riis for the 2002-2003 seasons. His time with team
Alessio–Bianchi in 2004 also didn't re-ignite his performance. He finally moved to the new
Saunier Duval–Prodir team for his last season in 2005.