Iannone and Avintia rider Hector Barbera were the only two riders who set times before the drizzle that began with the green light became proper rainfall.
Although the shower did not last, the track never dried out enough for Iannone and Barbera's slick-shod times to be beaten.
Marc Marquez got closest, but his 2m07.846s in third place was 4.667 seconds behind Iannone.
Championship leader Marquez edged out Honda team-mate Dani Pedrosa by just 0.002s to take 'wet track' honours, with the pair a second quicker than Valentino Rossi's Yamaha in fifth.
Cal Crutchlow went well in the wet, putting his Ducati sixth ahead of Jorge Lorenzo.
Barbera had the session's only accident, crashing in the final minute, while Iannone had his own trip through the gravel but stayed upright.
With rain a possibility throughout the weekend, everyone went out for a decent amount of wet running rather than hiding in the pits, the whole field completing at least 10 laps each.
FIRST PRACTICE REPORT
Marc Marquez (afp)
Marc Marquez narrowly edged out Jorge Lorenzo and Dani Pedrosa in the opening MotoGP practice session at Brno.
Although Marquez's Honda was in front for most of the morning session in the Czech Republic, Lorenzo did pop his Yamaha ahead for a spell with a 1m56.840s.
Even when Marquez did return to the front, it was by only 0.037 seconds over Lorenzo, while Pedrosa was just 0.015s behind the Yamaha on the second Honda.
Aleix Espargaro put the Forward Yamaha fourth, ahead of Valentino Rossi on the other factory version and Stefan Bradl's LCR Honda.
Andrea Dovizioso was top Ducati in seventh, though Pramac's Yonny Hernandez made good use of a lap on Rossi's tail to slip in 0.021s behind the Italian in eighth.
Tech 3 duo Pol Espargaro and Bradley Smith completed the top 10.
Ducati is back up to five bikes this weekend with test rider Michele Pirro making his latest appearance on a third works entry. He was 11th.
Alex de Angelis began his MotoGP return in place of Colin Edwards on the second Forward bike with 19th place.
- Sports & Recreation
- Dani Pedrosa
- Marc Marquez
- Hector Barbera
- Valentino Rossi
- Jorge Lorenzo