Hill, who gave the Virgin Mobile Samsung Yamaha team their first victory in some 14 months, could hardly believe his good fortune in the opener - he was running third as the Airwaves Ducati team-mates Haslam and Lavilla dictated terms.
Lavilla took the lead on the penultimate lap but then Haslam made a daring attempt to regain the advantage at Park Corner next time around. In the end both riders ran wide, on to the grass.
"I had nowhere to go. My bike was on the outside when Leon pushed through and across me - we both went straight on, across the grass and were very lucky not to crash," Lavilla said.
Glen Richards took third place for Hawk Kawasaki, ahead of Karl Harris, Ryuichi Kiyonari and Haslam, with Rutter, complaining of a lack of rear grip back in eighth.
Haslam, starting from pole, led the second race, with Lavilla moving into second place and running less than half a second down.
"I could have tried to pass, but it would have been risky," he said.
Rutter crashed out of fourth place at Chris Curve as his HM Plant Honda team-mate Kiyonari overcame Hill to take third place.
Lavilla leads 326-324 over Rutter in the Championship standings, with Kiyonari a further seven points down.Reuse content