Gatto took the win quite easily, outsprinting Swift and Raymond Kreder (Roompot-Oranje Peloton) in Padul in a race where the breakaway almost took the win.
Together the pair made it to the final two kilometres before being swallowed up by the bunch, which had been reduced to around 50 thanks to the climbs that littered the third stage.
As the group took the final corner, Team Sky came out near the front with Vasil Kiryienka working for Swift, but Gatto and Tinkoff had the beating of everyone, with the Italian cruising to his first victory since joining the Russian team at the start of the season.
Vuelta a Andalucia Ruta Ciclista del Sol stage three, Monachil – Padul (157.9km)
1. Oscar Gatto (Ita) Tinkoffm 3-53-17
2. Ben Swift (GBr) Team Sky, st
3. Raymond Kreder (Ned) Roompot-Oranje Peloton, st
4. Tim Wellens (Bel) Lotto-Soudal, st
5. Fabio Felline (Ita) Trek-Segafredo, st
6. Brent Bookwalter (USA) BMC, st
7. Simon Geschke (Ger) Giant-Alpecin, st
8. Philippe Gilbert (Bel) BMC, st
9. Reto Hollenstein (Swi) IAM Cycling, st
10. Mateo Busato (Ita) Southeast-Venezuala, st
Overall standings after stage three
1. Ben Swift (GBr) Team Sky
2. Raymond Kreder (Ned) Roompot-Oranje Peloton
3. Reto Hollenstein (Swi) IAM Cycling
4. Philippe Gilbert (Bel) BMC
5. Fabio Felline (Ita) Trek-Segafredo