A 90-degree corner in the final 200m caused a few problems in the bunch and Sagan’s slight hesitancy saw him too far back to challenge the South Americans to the line.
The win is Richeze’s first individual victory since the 2012 Tour of Japan, with the Argentine mostly working as a domestique in recent seasons.
The peloton judged the catch of the breakaway to perfection, reeling in the remaining riders just inside the four kilometre mark. Etixx-Quick Step and Orica-GreenEdge were pulling hard on the front for Gaviria and Magnus Cort Nielsen respectively.
Team Sky were also at the front for their sprinter Danny van Poppel, and race leader Peter Sagan had two teammates to help him in the final kilometres.
Sagan kept himself on Gaviria’s wheel heading into the last kilometre. Van Poppel went into the final corner too hot and did well to keep himself upright as he removed one foot from the pedal and clipped the barrier.
Sagan, albeit in third wheel, was too far back heading round the final corner to be able to challenge the two Etixx-Quick Step riders on the finish line, with Gaviria easing up to allow his teammate the glory.
Sagan leads Jurgen Roelandts (Lotto-Soudal) by nine seconds in the general classification, with the race heading towards the mountains. Stage five sees a summit finish in Cari where the race favourites could come to the fore.
Tour de Suisse stage four, Rheinfelden – Champagne (193km)
1. Maximiliano Richeze (Arg) Etixx-Quick Step, 5-08-21
2. Fernando Gaviria (Col) Etixx-Quick Step, st
3. Peter Sagan (Svk) Tinkoff, st
4. Tom Van Asbroeck (Bel) LottoNL-Jumbo, at 2s
5. Jasper Stuyven (Bel) Trek-Segafredo, st
6. Magnus Cort Nielsen (Den) Orica-GreenEdge, st
7. Raymond Kreder (Ned) Roompot-Oranje Peloton, st
8. Andrea Pasqualon (Ita) Team Roth, st
9. Jurgen Roelandts (Bel) Lotto-Soudal, st
10. Warren Barguil (Fra) Giant-Alpecin, st
Overall standings after stage three
1. Peter Sagan (Svk) Tinkoff, 9-14-13
2. Jurgen Roelandts (Bel) Lotto-Soudal, at 9s
3. Silvan Dillier (Swi) BMC, st
4. Maximiliano Richeze (Arg) Etixx-Quick Step, at 17s
5. Ion Izagirre (Esp) Movistar, at 19s
6. Tim Wellens (Bel) Lotto-Soudal, at 20s
7. Gokra Izagirre (Esp) Movistar, at 23s
8. Wilco Kelderman (Ned) LottoNL-Jumbo, st
9. Michael Matthews (Aus) Orica-GreenEdge, at 24s
10. Geraint Thomas (GBr) Team Sky, at 25s