The Swansea-based region were 28-20 winners over the Dragons at Rodney Parade with tries coming from Mat Protheroe, George North and Scott Otten.
Fly-half Stephen Myler added 13 points with the boot.
It meant after losing to the Scarlets, Booth’s Ospreys bounced back with consecutive wins over Cardiff Blues and then the Dragons.
“It was a tough derby arm wrestle with two teams that went for it which was great for people to watch,” said Booth.
“The Dragons were big and physical and created a lot of problems for us.
“It was fantastic to get the win but disappointing not to get the bonus point at the end.”
Dragons scored tries through Jared Rosser and centre Jamie Roberts who had a fine match.
Dragons director of rugby Dean Ryan: “We have to be critical of ourselves. I felt in the first half we did not put enough pressure on the likes of Protheroe.
“In the second half we had the ambition but we were not accurate enough after having plenty of time and opportunities in their half.
“We were just not sharp enough or have enough quality at the moment.”
