Hamilton completed the 3.7-mile course at Silverstone in 1 minute, 29.607 seconds, Saturday after Rosberg had taken the lead with a lap of 1:30.59.
Hamilton, who claimed his second pole of the Formula One season, said he fell into a comfortable groove in the third qualifying lap.
"My lap in Q3 was a lap for the fans out there around the circuit," he said. "I haven't been feeling comfortable in the car all weekend, so I was really happy to find a good lap."
Mercedes has claimed the front row three times this season.