To create a differentiating factor between the British and 70th Anniversary grands prix which were both run at Silverstone, Pirelli had supplied tyres one step softer than last weekend, and it quickly became evident that this change had hurt Mercedes.
Verstappen had started on the hard tyres while Mercedes ran the faster medium rubber, but the lead duo could not shake the Red Bull driver.
Suffering with extreme blistering, Bottas and Hamilton pitted for hards after 13 and 14 laps respectively while Verstappen waited to lap 27.
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Bottas retook the lead as the Dutchman pitted, but his fresh medium rubber saw the lead again change hands less than half a lap later as Verstappen drove around the outside of Bottas at Luffield.
The stint was a short one as both Bottas and Verstappen pitted again just six laps later for hard compound tyres to take them to the end of the race.
Hamilton returned to the pits for his second stop ten laps from the chequered flag for hard tyres, allowing the Briton to go on full attack in the closing stages.
The attack saw Bottas drop to from second to third, but Hamilton could do nothing about Verstappen.
In scoring a podium finish, Hamilton equals the all-time record podium tally of Michael Schumacher.
In defeating his team-mate and taking the point for the fastest lap, Hamilton extends his championship lead, but Verstappen also jumps the Finn into second in the standings.
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