Lorenzo, who this week signed a new two-year contract with Yamaha, eased to the win at the Northamptonshire circuit which put him 25 points ahead of reigning champion Stoner on the Repsol Honda.
The race was also a triumph for British rider Cal Crutchlow, who finished sixth despite starting from the back of the grid following a crash before qualifying on Saturday.
Crutchlow defied the pain from a badly sprained left ankle to beat a host of riders including Ducati's multiple world champion Valentino Rossi.
The British rider, who had started from 20th on the grid after spending most of Saturday in hospital getting his ankle checked out, said: "I'm a little bit emotional, it's been a tough weekend."
Crutchlow told BBC2: "I'm pleased, we did a good job. It was a long day yesterday [Saturday], they told me I wasn't allowed to ride at the hospital.
"It was a tough lot of laps and a shame I wasn't at the front of the grid because I would have been on the podium."
The sixth place moved Crutchlow back up to fourth in the standings after his Monster Tech 3 Yamaha team-mate Andrea Dovizioso pulled out when challenging for a podium spot.
Lorenzo had a poor start to the race and dropped back to sixth but gradually worked his way to the front where he battled with Stoner.
When Lorenzo made his move the lead changed hands five times in half a lap before the Yamaha man finally pulled away.
Lorenzo said: "I was fifth or sixth (off the start) so I did not want to make mistakes and I had to wait (to close on the lead).
"Fighting with Casey, I enjoyed it a lot. This season is just perfect."
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Stoner held off team-mate Dani Pedrosa for third with pole man Alvaro Bautista just missing out on a podium spot on the San Carlo Gresini Honda.
Fifth went to Ben Spies on the second factory Yamaha ahead of Crutchlow, Nicky Hayden (Ducati), Stefan Bradl (LCR Honda), Rossi and Hector Barbera (Pramac Ducati).
The win moved Lorenzo 25 points clear of Stoner, who has 115 points. Pedrosa is third on 101 and Crutchlow fourth on 66.