Giuseppe Rossi celebrated his new contract with a goal in Fiorentina's straightforward win over Belenenses.
Scrappy first-half goals from Federico Bernardeschi and Khouma Babacar put Fiorentina on their way, before an own goal from Tonel and Rossi's late strike sealed a 4-0 victory in Europa League Group I.
Bernardeschi's goal was a rare flashpoint in a sluggish opening quarter, the Italy Under-21 international anticipating Matias Vecino's parried strike to slot in to an empty net.
West Ham will face FC Astra Giurgiu or Romania in the Europa League third qualifying round after surviving penalties in Malta on Thursday.
The Premier League side played with 10 men for over an hour against Birkirkara after James Tomkins was sent off, and will resume their campaign at home next Thursday.
FC Astra advanced after a goalless draw with Inverness, going through 1-0 on aggregate.
Aberdeen are the only Scottish team remaining and will face Kairat Almaty of Kazakstan in the third...
Southampton will face Dutch club Vitesse Arnhem in the third qualifying round of the Europa League, while West Ham were handed a potential tie against Scottish Premiership side Inverness Caledonian Thistle should they both progress.
Saints finished seventh in the Premier League last season and so were among the sides for Friday's draw in Nyon, Switzerland.
The fixture will see Southampton manager Ronald Koeman return to the Netherlands, where he previously managed Vitesse before moving to England.