The Mid Wales star left round seven "happy" after claiming a third and fourth at Magny-Cours in France.
However, a weekend that began with so much promise for Newport's Tom Booth-Amos – who secured his fourth-straight pole – ended in frustration.
Davies, 33, qualified in 10th for the opening race, one place behind his Aruba.it Racing – Ducati team-mate Scott Redding.
But after a good start he was soon up to fourth, having mastered the tough conditions better than many of his rivals, with Redding one position behind.
The Ducati riders went on to finish fourth and fifth in the points-scoring Superpole race before heading into the final battle of the weekend.
And it turned out to be a fantastic race, held in very tricky conditions as the rain had given some respite, letting the Magny-Cours circuit dry out, before falling again a few minutes before the start.
Davies began well, overtaking fellow Ducati rider Michael Ruben Rinaldi on lap nine and then closing in on the leading group.
Between laps 11 and 14, the Presteigne rider managed to recover two seconds from series leader Jonathon Rea, overtaking him with seven laps to go, defending his position to take third.
Team-mate Redding claimed first to secure another double podium for the team.
Davies said: "I was very satisfied with the result. The feeling with the bike has been really positive all weekend, and for this I want to thank my team for the work done in these days.
"The start was good, and I pushed hard to get Michael Van Der Mark. Then I had a good duel with Jonny, and I'm happy to have finished with this good result."
The weekend also looked promising for Booth-Amos at Magny-Cours after securing another pole in the World Supersport 300 class in France.
But disaster struck as the 24-year-old had a nasty crash while leading the race in very wet and cold conditions.
Fortunately, he escaped from injuries but the RT Motorsports by SKM – Kawasaki rider's race was over.
Booth-Amos again started on pole for race two and with some sun starting to show, tyre choice was a big gamble.
All three RT Motorsports by SKM – Kawasaki riders decided to start on slicks but when the rain started to fall again, if left them powerless to perform.
Booth-Amos managed to bring his bike home in 26th while team-mates Tom Bramich and Nick Kalinin did not finish the race.
Team manager Rob Vennegoor: "Sometimes you win, sometimes you lose. I think that summarised our weekend.
"We had the race pace to score some very good results, but with all the bad luck we had it was impossible to show our potential here at Magny-Cours.
"A real shame, but that’s also racing."
The final rounds of both World Superbike and World Supersport 300 take place at Estoril, in Portugal, October 16-18.