Jonathan Rea extended his lead in the World Superbike series to 133 points by winning race two at Misano after taking second behind Kawasaki team-mate, England's Tom Sykes, in race one.
Sykes led all the way to win the opener at the Italian venue, with Rea pipping Welshman Davies for the runner-up spot.
Rea, 28, made it 11 wins from 16 starts by taking victory in the second race by 1.29 seconds from Davide Giugliano.
Leon Haslam completed the podium, with Davies fourth and Sykes back in fifth.
Sykes, 29, finished 3.613 seconds ahead of runaway championship leader Rea in the first race after the Northern Irishman's gamble on selecting a harder rear tyre failed to pay off.
Ducati rider Davies duelled for second spot with Rea before running wide on the last corner.
Home rider Giugliano had to settle for fourth after holding second place until two laps from the finish of the 21-lap race.
Haslam and Max Biaggi completed the top six after six-time champion Biaggi had touched Sylvain Guintoli on the first lap.
It was Sykes' third victory of the season, but he was unable to repeat that form in the second event, in which Biaggi again finished sixth.
Rea, who had qualified fourth fastest on Saturday, made up ground on early leader Giugliano and hit the front with eight laps remaining.
"I knew I had the pace all weekend but I made a calculated gamble with my tyre in race one which didn't work out. I put on a softer tyre for the second race and all went well," explained Rea.
The championship now takes a four-week break before the next round at Laguna Seca on 19 July.