Rossi's bike slowed at the end of the main straight less than 10 minutes into the session, his Yamaha reportedly suffering a broken rear sprocket. The Italian was able to continue soon afterwards but ended up only 11th.
With a risk of rain for both FP2 on Friday afternoon and FP3 on Saturday morning, riders put more focus on setting a fast lap in FP1 than usual.
The three Ducati GP18s controlled proceedings early on with Danilo Petrucci, Jorge Lorenzo and Dovizioso all taking turns in first place.
However it was Marc Marquez who led the way with a 1m24.411s before a mid-session lull, nearly four tenths quicker than second-placed Dovizioso.
The Italian started a run 25 minutes into the session which saw him improve his own best time, and consequently close the gap to Marquez on a couple occasions before he eventually took over the lead with a 1m24.295s.
The top two remained unchanged until the final minutes when Dovizioso improved by nearly two tenths, only to be narrowly outpaced by Lorenzo.
However, as the chequered flag fell, Dovizioso lowered the benchmark even further and ended up topping the session with a 1m23.830s.
Lorenzo was 0.215s off the pace in second with Petrucci, nearly half a second off the pace, completing a Ducati 1-2-3.
Marquez was best of the rest in fourth, 0.581s slower than Dovizioso, with Suzuki's Andrea Iannone taking fifth.
Honda duo Dani Pedrosa and Cal Crutchlow were sixth and seventh respectively with Avintia's Tito Rabat bringing a fourth Ducati into the top 10 in eighth.
Yamaha had a low-key session with Johann Zarco only ninth on the Tech 3 bike, closely followed by factory pair Maverick Vinales and Rossi, both more than a second off the pace.
Aleix Espargaro was the top Aprilia in 12th as the sole KTM of Bradley Smith took 15th.