The Belgian team took their first win through Yves Lampaert on stage two, where Trentin finished second.
>> Subscribe to Cycling Weekly this Autumn and save 35%. Enjoy the luxury of home delivery and never miss an issue <<
The Italian went one better though as he beat Juan José Lobato (LottoNL-Jumbo) to the line after the Spaniard had begun his sprint with 250m to go.
Trentin stayed tucked in behind Lobato, and was able to jump to the left nearer to the finish to easily take the victory.
Quick-Step had provided the most organised lead-out from any of the teams for their sprinter, taking it up on the front of the peloton in a very technical final kilometre.
The twists and turns stretched the peloton out, but Trentin was able to hold place among the other sprinters towards the front of the bunch.
As they turned right on to the slight uphill finish Lobato launched his sprint, but couldn’t do enough to hold off Trentin behind.
The victory means the 28-year-old Trentin, who is heading to Orica-Scott for 2018, has now taken stage victories in all the Grand Tours.
Chris Froome (Team Sky) retained his overall lead as the general classification top-10 remained unchanged after the stage.
How it happened
The day’s main break contained five riders including Johan Le Bon (FDJ), Stéphane Rossetto (Cofidis), Diego Rubio and Nicholas Schultz (Caja Rural-Seguros RGA) and Juan Felipe Osorio (Manzana Postobon), who established a maximum gap seven minutes.
Aqua Blue Sport did much of the work to control the gap through the day, with the time steadily declining heading in towards the only climb of the day.
And it was on that climb that things fell apart for the break, with Rossetto jumping clear with Rubio as things began to slow and cooperation between the break faltered.
Those two pushed on and held around 1-20 within the final kilometres as Sky and Quick-Step worked on the front of the bunch.
They were eventually caught with 8km to go as Quick-Step ramped things up on the technical run-in to town and things were set up for the sprint finish.
There were a number of crashes on the way in to the finish. Sunweb’s overall hope Wilco Kelderman took a nasty tumble on the narrow roads with just under 20km to go.
While he was able to continue, Daniel Moreno (Movistar), Domenico Pozzovivo (Ag2r La Mondiale) and Jelle Wallays (Lotto-Soudal) all came down in a nasty crash at 3.1km to go, just shy of being given the same time as the main peloton at the finish.
All of them were also able to continue, albeit Wallays very gingerly got back on to his bike to ride the final 3km.
The Vuelta a España continues on Wednesday with stage five, a 157.7km route from Benicàssim to Alcossebre.
Vuelta a España 2017, stage four: Escaldes – Tarragona (198.2km)
1 Matteo Trentin (Ita) Quick-Step Floors, in 04-43-57
2 Juan José Lobato (Spa) LottoNL-Jumbo
3 Tom Van Asbroeck (Bel) Cannondale-Drapac
4 Edward Theuns (Bel) Trek-Segafredo
5 Jens Debusschere (Bel) Lotto Soudal
6 Sacha Modolo (Ita) UAE Team Emirates
7 Lorrenzo Manzin (Fra) FDJ
8 Søren Kragh Andersen (Den) Team Sunweb
9 Youcef Reguigui (Alg) Dimension Data
10 Jetse Bol (Ned) Manzana Postobon, all same time
General classification after stage four
1. Christopher Froome (GBr) Team Sky, in 13-37-41
2. David De La Cruz (Esp) Quick-Step Floors, at 2 secs
3. Nicolas Roche (Irl) BMC Racing, at same time
4. Tejay Van Garderen (USA) BMC Racing, at same time
5. Vincenzo Nibali (Ita) Bahrain-Merida, at 10 secs
6. Esteban Chaves (Col) Orica-Scott, at 11 secs
7. Fabio Aru (Ita) Astana, at 38 secs
8. Adam Yates (Aus) Orica-Scott, at 39 secs
9. Domenico Pozzovivo (Ita) Ag2r La Mondiale, at 43 secs
10. Romain Bardet (Fra) Ag2r La Mondiale, at 48 secs