Serbia are bidding to reach their third final in the premier men's team competition and first since 2013 while 1976 champions Italy are also looking to return to the title clash having last reached that stage a quarter of a century ago.
Musetti made a slow start against the high-flying Kecmanovic and narrowly avoided going a double break down, before the world number 27 found his range to level the first set at 5-5 and come from behind again in the tiebreak to clinch it.
But Kecmanovic's level barely dropped following the setback, as the world number 55 breezed through the second set and broke twice in the third for a 4-0 lead, which was enough for him to see off an ailing Musetti battling a thigh issue.
The top-ranked Novak Djokovic can clinch the tie for Serbia when he takes on world number four Jannik Sinner - the hero of Italy's quarter-final comeback against the Netherlands - in a rematch of their ATP Finals title clash in Turin.
Sinner lost to Djokovic in that match on Sunday but beat the 36-year-old earlier in the season finale in Turin and looked in superb touch at the Martin Carpena Arena two days ago.
Serbia, who outclassed Britain in the last eight, will need Djokovic and Dusan Lajovic to defeat the pair of Simone Bolelli and Lorenzo Sonego if Sinner forces a doubles decider.
The winner of the tie will face Australia in Sunday's final after Lleyton Hewitt's side beat Finland in the semi-finals.
