Mid Wales star Davies had double reason to celebrate as he followed up a third-place finish in race one with his first victory of the campaign, moving him up to third in the championship standings.
For Newport's Booth-Amos, his victory was his first on the world stage and he nearly made it a double win but, whilst leading the second race, he was taken out on the last lap.
The 24-year-old was in imperious form all weekend, qualifying on pole and then claiming the opening World Supersport 300 race at Circuit de Barcelona-Catalunya on Saturday afternoon.
Heavy rain had created some tricky conditions but Booth-Amos managed to claim a dominant victory by more than six seconds at the circuit, which is now a home-from-home for the Shropshire rider, who is based in Barcelona.
His victory also marked his Dutch-German backed RT Motorsports by SKM – Kawasaki team's first-ever WorldSSP300 victory too.
Full of confidence, Booth-Amos started race two from pole once again but while challenging for another win he was hit by another rider in the last lap while leading the race.
It was a massive disappointment for both the rider – who, thankfully, was not injured – and his team but could not detract from what turned out to be an historical weekend for all parties.
Team manager Rob Vennegoor: 'What can I say? Our first ever win in the World Supersport 300 championship!
"I would like to thank everybody who has made this success possible as this is a big team effort.
"We knew before Tom was fast at Barcelona, but winning a race is something else and it was an impressive master class on Saturday afternoon as the conditions were so tricky.
"The end of the second race was a big, big disappointment but we have shown that we can win races. Congrats to Tom for this great win. We can’t wait to race again in just two weeks’ time."
In the main superbiike races, the Aruba.it Racing – Ducati team also opened the weekend with a solid double podium as Scott Redding and his team-mate, Davies, 33, rose from seventh and 11th on the grid to finish second and third respectively.
Starting from the fourth row, Davies had soon caught and passed Kawasaki's Alex Lowes and Yamaha's Toprak Razgatlioglu, moving to sixth position, before taking the second Yamaha rider, Michael Van Der Mark and then grabbing the last podium spot, overtaking fellow Ducati rider Michael Ruben Rinaldi with three laps to go.
But then Davies was able to go even better in the final race of the weekend, claiming his first victory of the campaign, and Ducati's fifth of the season so far.
Having finished fourth in the second points-scoring Superpole, the Welsh rider quickly got to the front of the pack and never looked back, defending well from Van Der Mark's late challenge to take the win.
Davies said: "It was a great race. The feeling is that we managed to put all the pieces of the puzzle together.
"Maybe we did it a bit late but the important thing is to have achieved this goal.
"I would like to thank my team who also worked late last night to fix some things on the set up that worked out great.
"The race pace was very good from the opening laps and this allowed me to stay in the lead and manage the race. I am really very satisfied."
The World Superbike series now heads to Magny-Cours, in France, October 2-4.