Hill gradually began to break away from the chasing duo and led by 1.2 seconds after 12 laps, with Laverty beginning to shake off the attention of Brookes in third.
Lowry, Patric Muff and Walker were enjoying a private battle of their own in the closing stages of the race, with Walker on the Pr1mo Bournemouth Kawasaki picking off Muff and then Lowry to set up a thrilling last-lap duel with the Thruxton race winner.
Hill had established a cushion over Laverty and maintained the gap in the final laps to tie up his second victory of the season.
Laverty had the consolation of setting the fastest lap of the race in a time of 1m 49.343s to secure pole position for the second race, with the front row completed by Hill and Brookes.
Byrne, Haga and Lowes form the second row.
Haga got the better of Lowes for fourth, with Bridewell, Walker and Lowry the top eight.
Muff and Barry Burrell completed the top ten, while Alastair Seeley – involved in a huge crash on Saturday in qualifying – finished outside the points in 16th on the second Tyco Suzuki.
Luca Scassa, Scott Smart and Graeme Gowland all crashed out of the race on lap three.
After race one at Snetterton, Hill heads the standings on 123 points from Brookes (108) and Byrne (88), with Lowry into fourth place on 60 points.
to view race one results