The 167km stage from Reggio Emilia finished as expected in a mass sprint and Gaviria (QuickStep Floors) once again proved his pedigree as the fastest man in the race.
Ireland's Sam Bennett (Bora-Hansgrohe) was second and Belgium's Jasper Stuyven (Trek-Segafredo) third as Gaviria added to his victories on the third, fifth and 12th stages.
The top of the general classification was unchanged, with Holland's Tom Dumoulin (Team Sunweb) in the pink jersey.
Dumoulin has a lead of two minutes, 23 seconds over Colombia's Nairo Quintana (Movistar) ahead of Saturday's 14th stage.
The 131km route from Castellania to Oropa features a summit finish, when Dumoulin's rivals could seek to regain some valuable time.
Bauke Mollema (Trek-Segafredo) is third, 2mins 38secs behind.
Team Sky's Geraint Thomas is no longer in contention, however, after he was forced to withdraw ahead of Friday's stage as he continues to struggle with knee and shoulder injuries following last Sunday's crash caused by a stationary police motorbike.
That saw Thomas enhance his hopes of a top-five finish, or possibly even a podium, but the pain was too much and he has now refocused on supporting Chris Froome in July's Tour de France.
The race against the clock also saw Dumoulin prove his credentials for overall victory in Milan on May 28.
But the overall hopefuls were able to keep their counsel on Friday as the sprint trains controlled the peloton.
And Gaviria came from behind to go up the right-hand side of the road and win by half a bike length from Bennett.
Stage 13 result:
1 Fernando Gaviria (Col) Quick-Step Floors 3hrs 47mins 45secs
2 Sam Bennett (Irl) Bora-Hansgrohe all same time
3 Jasper Stuyven (Bel) Trek-Segafredo
4 Roberto Ferrari (Ita) UAE Team Emirates
5 Ryan Gibbons (SA) Dimension Data
6 Rudiger Selig (Ger) Bora-Hansgrohe
7 Sacha Modolo (Ita) UAE Team Emirates
8 Caleb Ewan (Aus) Orica-Scott
9 Andre Greipel (Ger) Lotto Soudal
10 Viacheslav Kuznetsov (Rus) Katusha-Alpecin
Overall standings:
1 Tom Dumoulin (Ned) Team Sunweb 56hrs 28mins 53secs
2 Nairo Quintana (Col) Movistar +2:23
3 Bauke Mollema (Ned) Trek-Segafredo +2:38
4 Thibaut Pinot (Fra) FDJ +2:40
5 Vincenzo Nibali (Ita) Bahrain Merida +2:47
6 Andrey Amador (Crc) Movistar +3:05
7 Bob Jungels (Lux) Quick-Step Floors +3:56
8 Domenico Pozzovivo (Ita) AG2R La Mondiale +3:59
9 Tanel Kangert (Est) Astana same time
10 Ilnur Zakarin (Rus) Katusha +4:17
