Having worked his way into a good position in the peloton going into the final kilometre, Trentin bided his time in the tricky closing sector before bursting clear of Juanjo Lobato (LottoNL-Jumbo) and Tom Van Asbroeck (Cannondale-Drapac) in the final metres.
Dimension Data's Merhawi Kudus of Eritrea finished second. Nicolas Roche, David de la Cruz, Fabio Aru, Vincenzo Nibali and Romain Bardet all lost even more time to the four-time Tour de France victor.
Lampaert took the red jersey thanks to the 10-second bonus picked up for the stage win, his first in a grand tour, and leads the general classification by one second over team-mate Matteo Trentin.
Team Sky's Froome has a 10 second advantage on US rider Tejay Van Gardener, with an overall time of 18:07:10, with the Briton looking in impressive shape after his Tour de France triumph.
"After my crash at the Tour de France I was thinking about coming here and winning stages". "And if you think there's just a 3 kilometer climb to the finish, I can definitely be happy". Two days ago we did a flawless, smart job with Yves Lampaert, and [he] took the win and the jersey. The guys were incredible.
"This is the biggest win of my career, no doubt", said Lutsenko.
Two riders, Stephane Rossetto and Diego Rubio, led a breakaway that was neutralized by the peloton with less than 10 kilometers (6.2 miles) to go.
Asked how it felt to complete his Grand Tour set of wins, Trentin, who will join Orica-Scott on a two-year contract at the end of the season, said: "I'm really proud to do this with Quick-Step".
However, Alberto Contador lost a further five seconds on Froome in his final race before retirement to fall 31 seconds back on the four-time Tour de France victor. David de la Cruz (Quick-Step Floors) +0.02 3.
But others were less fortunate with veterans Daniel Moreno (Movistar) and Domenico Pozzovivo (Ag2R-La Mondiale) among a handful of riders who crashed heavily on the outskirts of the famous seaside resort of Tarragona inside the final 5km of the race.