Stanislas Wawrinka and Marco Chiudinelli had looked on course to earn their side a place in the final, but Italy's pairing stormed back to record a 7-5 3-6 5-7 6-3 6-2 win to leave them 2-1 behind their opponents going into the final day of their semi-final tie.
After a competitive opening 10 games, it was Italy who struck in the latter part of the opening set by breaking Switzerland's serve for a second time to edge into the lead.
However, Bolelli and Fognini lost their way in the second, making 16 unforced errors to allow Chiudinelli and Wawrinka to break serve and level the match at one all.
The third set saw no breaks of serve until the 11th game, where Switzerland took advantage of some indecisive play from their opponents to steal the advantage and move one set away from a place in the final.
However, despite letting slip a one-set advantage, Italy continued to fight and they were impressive behind their serve in the fourth, dropping just six points to ensure that the match would go the distance.
Switzerland were beginning to wilt and Bolelli and Fognini took advantage to ease through the final set to take the tie to tomorrow's final two rubbers.